From 4b96667b181b5e92abacad921c58b8da5ff62f83 Mon Sep 17 00:00:00 2001 From: Sven Riwoldt Date: Sat, 7 Nov 2020 21:22:50 +0100 Subject: [PATCH] Erste Grafik, Versuch eines Skripts, etc... --- Linear Algebra Refresher.md | 16 +++++++++++++++ convert_pdf_to_png.sh | 5 +++++ vector.py | 8 ++++---- vektor_add.pdf | Bin 0 -> 19680 bytes vektor_add.png | Bin 0 -> 14041 bytes vektor_addition.pdf | Bin 0 -> 19207 bytes vektor_addition.tex | 39 ++++++++++++++++++++++++++++++++++++ 7 files changed, 64 insertions(+), 4 deletions(-) create mode 100644 Linear Algebra Refresher.md create mode 100644 convert_pdf_to_png.sh create mode 100644 vektor_add.pdf create mode 100644 vektor_add.png create mode 100644 vektor_addition.pdf create mode 100644 vektor_addition.tex diff --git a/Linear Algebra Refresher.md b/Linear Algebra Refresher.md new file mode 100644 index 0000000..62fa50d --- /dev/null +++ b/Linear Algebra Refresher.md @@ -0,0 +1,16 @@ +Linear Algebra Refresher + +Addition von Vektoren + +$\left[ {\begin{array}{*{20}{c}} +1\\ +2 +\end{array}} \right] + \left[ {\begin{array}{*{20}{c}} +3\\ +1 +\end{array}} \right] = \left[ {\begin{array}{*{20}{c}} +4\\ +3 +\end{array}} \right]$ + + \ No newline at end of file diff --git a/convert_pdf_to_png.sh b/convert_pdf_to_png.sh new file mode 100644 index 0000000..88a79d1 --- /dev/null +++ b/convert_pdf_to_png.sh @@ -0,0 +1,5 @@ +!#/bin/bash + +pdfcrop $1 $2 + +convert --density 300 $2 \ No newline at end of file diff --git a/vector.py b/vector.py index 8c74354..3445546 100644 --- a/vector.py +++ b/vector.py @@ -11,10 +11,10 @@ class Vector(object): self.dimension = len(coordinates) except ValueError: - raise ValueError('Die Koordinaten dürfen nicht leer sein') + raise ValueError('Die Koordinaten dürfen nicht leer sein') except TypeError: - raise TypeError('Die Koordinaten müssen iterierbar sein') + raise TypeError('Die Koordinaten müssen iterierbar sein') def __str__(self): @@ -43,7 +43,7 @@ class Vector(object): return Vector(new_coordinates) def magnitude(self): - #Länge + #Länge coordinates_squared = [x**2 for x in self.coordinates] #pdb.set_trace() return sqrt(sum(coordinates_squared)) @@ -72,7 +72,7 @@ print (vektor_2.minus(vektor_3)) print (vektor_3.times_scalar(3)) -print ("Magnitude -- Länge ", vektor_3.magnitude()) +print ("Magnitude -- Länge ", vektor_3.magnitude()) print ("Normalisieren ", vektor_2.normalized()) diff --git a/vektor_add.pdf b/vektor_add.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c7856cc289960392b1575bb1c5b91d3fe12f7344 GIT binary patch literal 19680 zcma&Mb8u!+vp4$0wr$(CZQGM%V%rlZ6Wf~D_QbYr+sTvU&U@}Tx4v8VtNQN#V^{au zy;gU1*Y2+F^`lT0mt!ZGlDDw8a{WQf#zXwy4=j_U z^-os|XJRJFpC+yr;udBO<`%Gmg0L>G&K4$iu%7F5hpg(%08udr12Hr>2m>`Xm#{;9 zM!y+-F^DwZ8ev9&oit=GtcAV#fA9E5{YM+i|Dsjh%h7_ENn6R(#=^`MmPyUc)b+ns zBpsaX{u%J^{a+F+uuRJ8655RaEV58Ev9lniW@K`=uyu8CHZn0cw|2F5uxE5Mx1{-R zF=Z1g3q?0O(|^YQ&rTV8O9ydlGgo4+f7(@HnM6e$Jc;#~|1q2_ti)VAtOl@5sunH| zZq8;FF2w(Fh?v7q2WK@$6ElndVjZn49i6RAiS?M2Od3rQ28S&%wZ6_o$@l>;wt>A_&3&zc!MprlbbGz1|5g7uKF9UKG!Lnl^nN#iW^^dYNc;1}Yv*B7!d0FRoDVEYVkHupZ zYh@glrQ;*D5?Sx8&EJe8Atu&3?c6g#G~+HYiDTk)xkLSQIN3xq8U; zY0LHZI2sTHle#z>hr#1B1k~7L%hm?U60?8PwRuYvSgK%kS7!>%rC_!&dMON+Wv~#k zbZGd_y0!F6W=tg^=u$`sywwv7vvBv0+^#Lo8BJ%0J~G!{Hh(&w2t=6u__S7aWKQu{!7lHd%myx+s+a0 z-sY#8tmE%>&&3=b3V2y1)1Z|oG$@a|JUX)D87NFpDy$8=T=v>-q}9CR#OzWhjwFnIXf$e$sJhYQKjLj_ zn`byPT6=wXzJ84m7skZpcml~;sm%z5qF#_5j|UEv!ifkk7+Lf4&lV?}aQQTBmGF}B zP0zOslGArTkZaV&^W#wClO-30tvTGoRmJPg{D>&bN*3J1=V8yO&)8(aZ1S6MJH;Zg zZ8x^kye^w#OsF1M{~VZ4b0ho-QfqOKPhOgz^=mJ~kelLbPZJ@a;Y-9-AuC^67f=l< z_IR<#8#derDn45%OO59w;41&;3xTTqYR9RdB4;7~9by^AqSL)qHsoU8e+)=WUFJ?O z#eEd2I!rC8mlhZyUkkgE?FnW*7NsCk1}hp`F30uBK;HKfB0?)6^U0ZsT4OvQv&mAb zZ+53{*I@iSZ;;>$Zt+lL+Bn%6+{1EurAOpm79Y+V&91RQmxX)$)1Q2QD#~rqD0*3|+r>X$5_vy`e;sBp`U+ELbIczWDo*`Wxqt7%F`>2T9sn#n-JB4~Na< z_F_{@uhsG8T>SJ9P~&V4yb8vDKlc*T_|a>`x@9>b|0%})V{MkS+hzv8cP2~Qwp@L^ zh^4XK?M9qzo_z(E2EK^($2R}Bw;8DrkjJ4w$6>>!HWP2?O0z>X9X5QSRH!MbAGONy z)Cobq;|vMGf;J=kpr><&1YI~~UNSOg!+YIbTJ)`tG^9Z+IN00bJkY+uor?SzGVo(XYWO;>!pz>Se4$v5`q_d)WE&~@rQk(d= zNqyOZe=va5FZYXXj;-I)qKd99J+DFyJ$le_ef@%pUkD@O_+=y?m3h~i-3ubU^FjZ= zDQN%SI?6)K!p_b9KiT_Vf#GKRm%jh+8p}q^{68cyH#ZyC|2eJ4HbJN-8(?wDmqoY^ z%o2#Dxq5^j0>I!A*_h!GKv79aP)Qle*;P@46X&Q@Ks_$Ba| z+rU1P#BY@R2tdg1mvmHUFQPJpa1eI>0zf`8fSMKtJqaBd01XQ*4WvVk`wdPV)J2R4 zuoDb~#D{$DGt&s|d?O`RoF4tK`)USvTy+5rL`5~_510qJuQ3K6Bm@Wh5%PQ5c;$oO zN<=x3WRnn7^8HH-2GQDzd|n|jZ)am83+eE@A4-aQ%<&%3MIvn#2(k(ma|_A`@JE9@ z4b<-sU^y5tgTUqy8a~s#>x5EGmsEZ>|;cx#!><%`h(+hYd-6w%F(%vVY z3n&=~DJUqYDXJ)-jt_8Yb~E|i*_BX>_ZpA(iq~U>e0l@v0mi+Z1b`C7?|%vK{30Y~ zVg^Lsf}#_&~b-);SMQ z{rX1#>Ky-8IQ-uD9YuxyJ~DMT^8M`;qEDi{(+hSjaS_=?1h9Mk#P0jzT0{q~%-Vzy z5a-r>UuZ}LUqguy9)o|LV3QEiA`{hx5Q1CZ0Mm58{>BC<;h=+pUGxhO_vT>$Za$ZQ z@i+cWmwDSl1cWb%zyr`7rRe~Na`?t@J|H2B2#N{-ItcK#zh!jaO#ylfwLMb^wt5mD z0Rr@8=Drt%a8zPK-i4Oh{p?XeAp!J~9U3;joEio03IJZjfnd;bfY+P6+JKE09D8M@ z_yDU2z^g!?;mgdRP{gf(Gt*AMPvStLvlzhl2qWlA1Q#&=)5!Ny043rh;j5_4r{TNd zyNk%U4r!Ip!4lP;3FBB5W7+jiC3iT>!|e7B`{I{1ELH6{eBs)|Imt8LbX3fVTm;)2 zmw;XT@k%m};*lkeJk}w5s`d!ESc_Y=cAdMA^yDnV*u|&rSHTy3@=iv{^~gmh&T&^8E#+kvYep|77}I#X zYN4piYC__5=GYby?+ZPmG&3BrgRsT&W6uT|NG{B%xqNc1T* z5%Dv*Eg*Et$b?TP#B{v3&iHGiNh!n?WPlGexAmbb{jmn+p}*L7NcVPK2E{z<$+BX@C#aH#6u5|NpgBwywetrLSUY|8>s znIyQM@#IbB9}5GU_8jmfwikulmdQkXD~{ht(46-yOwPAEQrXwAPL{(oaUiay>|k0s z+o`OQ!`E5s5FdA6o*kBK$41KSJfEUxbWA^7e<7z4WIG}j{T81(G5VGq<%`pVswq(# z;98FkU0K=UAfNIgt|R#3)}B0iz{gC(_65`>SITqpW6Ja}?&K`iBVq3n+n+S?d8#TF z@6Y@RW$)~zeoRn4`(QI9O;3MvgcY*u!9dtiUU5J7<7Q@sa^2}F{UsK?3)|pgA6g-n z(5M=rsjK(-m_}2})PgB}?s{=E!5@X$jH6n8R`H2NI}UhcZBS>d(Rd93H69Wp1y`%h z#(6TEVVCK1F7LmoN;iv*YjDW=!BEts6pL8J@*G=L|0*^?F9hwe2v#g^sybJ2_cKP# zw%?jcE}qA<(4L^^94of_$kx)DZegT1DDAo9g9SakJ}V4d+5+-r5%4B)i4(00v03bq z6sf~l>7U`O1@H6}KOsP0i7BI0G9X8&*OFe;KuT>c@hu!A zGWWMLq8WCrIRy&e-2GJ@Pz>QOtl(ru9IZsG2s(l}3#?veFZQzSoGkw_a?;-OUg}n) zOfyX8VA7AT!tHQcHN|atT2dLOZ6SCv9Z=e9(cSm?5WNtGyF00$d47r0#Za*55WB_O zG6CC80#)Um+0)vWPJ+6Vh*Co|6E&bqp7019Qu)9?^3g!{&82=v7dRlQR>Iu+=pr~R^KvQ^33NFH2=lT6fj3I zUMw>a?GC`*&+$>hO+sEeaCt12FH&()=0lO@A)^+It|uc`JKU=ve>d08|z5+WAZ6CzcDu7{7`ZK!gw$7r&O*bYP$fH z#m?+o)KS6$pE*v}&$;!=g1Ee1V{OUK?WxEt1^P8a-qfh4v$v4O4yzlj_cq9a@O+bydLVYIJw`>+w`6rtK@90*k1DVJUUH2ROUffIxNDgp~5DeuuPEle%& z>fNC$xj^SEJRP?aLD88je25h=40_lx-CeQlGjpiyLVKgRhZBazXaFxp@Ly(GhV+QN zdM-Vbo9oq)D0+?FXwk@<=U)dgnF4;@00k`G1c+v-1c2 zXOHrpD0gq~9T;*@3s)WkZ7vGP1GC;vE0{a2BXT(E``qro)uv(5VAwM!tFi zdLU2|JCvUxLyjV`GN$x-2@6Wr-KkbPdnw27$fOj!aYgS&O*+bRS0Ol;1RS}j!`8F^ zBg8Syqy6oB-yEAw7WN0Zc|DPE)OIj_+%s_U_@EPH-a$z=@KJy0!k~T-!)blfz}>zd zMfD4A=(CN);$8G`gOXBpfky!>!3+r|V#4jswK0{1UtxcrBI&Wf=L%&{@rF=O&@k0Z zRi|fOy`6cy{v!qTdx-oHBN^;meLIuKmP;42vroI%fIoqM&Z^zn1qO8)O4au=0FpXE z+l`Cn&-bhmK>D`Mza#Hr@0OO}d6uaM1FDnWfzHS|QIl>We*7F`PK5p^<4MA=APBFlP|t_HIllP8|Zg~oxH%qC0NRB zn1cPcdjdW45B4fX;-LFni=hmp&BO3l`p^gXGKj0Lq_!)N(Lx{?0W(JlTeWJy5~x3w z8ZFsp;}a^4Jqy=_uLBXS>4Sy_{{;lf(S6X{l{l;Ex(DY2!dOM~37r&QKmOxAQob8G z8Iq%6}PohWrAoTbX@uV&F!BSz2yn>Ls zt5!Kcncm9lsxA@Q&ceD*VS+p*on^08vV%~Y7eOnk`MktnS+0Ty<~<2IxnaZa{_`n} z3G^T>f>Bc_p5q5mr{ujdUZ&w94xvKJc$uSSUm~T@Uw`zSjQ5mAPP4_krBZYaX&l=a z>^_>~GnJoDy(24WWdBX3vbk(?$W6$HP6-)qD2i=04xrIf>;@FvopaK%e0a6T9?_sQ zV0XQz2r9|M3qQq=j5FArSuTa+ZP zgjT1JMGoZ3fy{WTc&-T5_|CrgappW-71ftLd+c2ex&*ud3MuO)?PM2aXYSEvWkDGtsdNFKnlDyc}Vxt2!jk5wYb1}+|SDW zi!nhxeVE^CwC6R=C)KSv=_Jgq8c*i*&utE}+iZxtJnv3)q!?N^sjDcez9CxOo`% ziZ%kTb4Z1PJWfFRdy<6{uZZM&Y9kCHY4xYmDx?H+X5)l9R0@meF6SqPlh8#~39qNi zwx*m6Oi5ceY-;TV9O}S)BaeS0rG~OeHi}B|CLwiWdOO0&1VTxZq^@^;No_ea_1EYf z3L)Qi7s_xJ$2rb3W39-kWX`ruPe0Y2svrnCyR!jI6CqWB-YOWbKR&?@!`aW_o9r=F z;0eId;}gQ4g2f2oyV2KAxT=OwNm|i>RQyj(%mvGY&2>uO=}7j1XC2J9R_=0bz4!Qm zkFZQwCd_#8eu6yR6CB$8i#zkgmI9-vt$ngTa?T;c+o?U1?YMe!+ zX*q?I`53h}1pbQEd^|F7AMv9$a<{>X>Jv+$6odcOtu58Gt?&U9;JeU_g-R zht{M&)~4c;(N=cD z54X?lwRadxm1~yY?Zek9U3tScoCQ%CIZ2lpo!T8f%y03>==WN77P3t9!6j429)Sz~ z5vTFiZvtM7B&OEu0qsN9lH836g070h1UeyJplIXYg{55WhGCo=ABEQZSv2^MY8^Gk z7n;HM2FMHS>g51bZ+RX2mQMPOL)nT1N0DhhN_2NcD4i_Tq^tmfeQtE`hoY@ z;b?)jiIn(szdpxmg)^6L_{EpZAXWMV{+FP)vtm;>ow5tX>ZdYT4J8!3CD+U7b)4M~ zqfqIubSL1((dyR{S(n9LT1p?QcJUMwMTRgJ{k6h~DHV(rW=G{;MRmG%u`9U^>x(%^ zjVU&o1k@_uo0_c|?2B{g7qK@{5~;TnxnptUnfcw8u&3vPt>0-yG5ajg->&f*Rtf$wGxQrR;uANyCj>+yQl!UlC*AQ2c{oA#juhckRQ*u`*dABglBz0*$ zkT67DKcd=iJiKjCJ|m;ra8A3 z(oXZTE`%5x)11Vv5uwh{Blt>bf&DoXI&-QZbO{~J^V8M}qRLn#Aim{~1dhbbv@A`Y z;??=~fe}u2TLa`j$&5$9%dVfikr?yzm#g`O>L>VIBU}b{p~Kd85j=n8h!7tTyY~9y zeGAoU^&v7o`GS8nk|Mi;|aXAMGsO|9}9F-_#)G(#d@}EREbCV;W;Z^-&f#N?({%snzbeWlOn>bJz^i` z$GuD37w}Bs5Lx|oqI!qVX&@ghO~imYr4IaVG{S}s{t%JSU>){6XOr?f&k-OxQ6Y2;_Lr@$LJONSJf^aJZl0*|_30L^Sg z%jAayN*FML5wjJGe?e;Erw_Gt_512h>9X(vK3X%a ze1Pfd8doX5AkLXxOR!x{Sw3O2D!s4dIDUCjo!3cG+d5{=L#bE?m#+Y2a&2d- z%s}kn$K6>nx`h4~71Gb+JuLzWEw<(4zbvs6MqCC)J(q=z0j2ic)H7=J7*Tc9bj9Qt z`z;5RBIQCvfm!~`?!OBO1F5Jo%%E`L@8)vEoomydrEfxY8kX9La#DUOG^J{8j$#o2 zR3$1qufz=B$>TYtEhvd*`o|Nb4`+*4F(r4-7VeQ31{}G|1f)y zk>J-#x?MbTyz6V@O%orX3L2*nVjkIaa{u^|A+T69*J@jdMl_n!%3@usCA)gvf{8x4$Oo5D>(i*L3;ZX+EOhW_~7Bg4+a!g(Pm zvW@N7UTw!{d>0555gmuV>BUBL1yUiiMBZaaaAeTSdmg&*GvQ#|x8S-`pyqOtWK0cryorX_PD=W|5OT=(5Y$f}bf?lp)1mM&f_i`$i^=<%W zI{bUrLdNt>{k%XMmT{ujyJ1ujpE&a4y$$G@5~T=zB^X3t1%D&%#-qYh-3lj>+yN|C z!S1e#o`}zlEk>N?+Nng>9K9b>OlDhrq^L-oC~{2&dbOk5r1(eDTBo^q0ayrZbZSU7^1S|$DY437JN#ai*M#G?|G zt(6-gL}Cw`*8~=0gPTNC7KKHTE@7WU3A^J=k9c|GW-&*C^*#~Mjk5hhf_Ib6c%=x)!%IVKr zhDZGYF*>UdQ>`pA3$$aYU-Z~Mg9|+|pUh=9J5Q@O9bR0FNv>w%C1eoOA+qNUzXGp; z8#VlLR?6{@5v&+!_XC|nOT65pJ^I7I6bU_Sdpb>GNFm!m@F4N8v`7P;Eo^bU(!t)BQWgR=R1L43P*Tkd~n(w#QfokQ$ht`HDW=1Dt zv&7Qk`1{3(ALIj^w&!py-zUOj-|AxyGKM^IfuAZz7iWtxmNY!q22;XqZb%%dE{nO= z?U)(B%^^_>RX*T+jI)dKub#*zBO8NwTvFaX>c>02-Bvp7orIJIK{>pC-Y0JQy+W0M zWV`?FW0Fh?Wa5H5Kdi@e zK@$U__WE+&aKH!gBimA%^dYxchNC#dp`7DSSqG68c(je0ne%Bi1e9;JfDzhy&(Xgo zU`;ay(l4sqnQW2WzFXIX=!es9kBwREL9FGXpc)$>ksm3g#{UNO!toEi`2R+a{s;BK z%JV_D3l|&r{~y$g2b6l!MFZ!2afEt;qOkEo(rodIVM>K+5;Ad9 zDEYj|@9pI6EZ4Jc8MTT)Y6Uob zNm1DrX=;6fvnUKuxR7EHT5oS%V`Kn0Dh6bb_-I>uEQ+?(>yAIGy&5-eh;WDOHFq3zBqh9-tAy_ZKst3Vv3y<1dT( zCarWb7Ou%n;84!P3t1r6Fcd&eW(yOTf~f2qRD{ADK_`q9>=xL$s~9Sh4I(Lx4I20K zE(K$#14WNXfdKC9=?N{S&-_=qshdBKxDPDI4S@ZZ#j%NR6Vs80RhVcW^qVb{8HcNH z6(s15fLV0iM1c4QH{irkvTwHrTYp?kOOG2jkdMH)xCD+_xZfZk#4P{}93+4d3V;du zUAdWeIUx$YVl;+~4SyCK+~!T9e+A+WZN=RuY@mgG5s3jVtZ&B@glq+mnug>QPMl4m zjK8aOfgIQ|ZvX)2+RJ-mW@ZNs8-g}No=#%}Wt!Nn(V1G(ggDy=^%yc8W&BW+$lqh$ z?Dhfqre7JuINLjaXtfA;Y;NwvA9yB#{jneA=mWi?`We#SKKgal7;Xl#Pdv6!n79vU z!vkEyxBv_ZjW5H3zhQ%!w%TxjzRJ?*eTZC;n@A>5BYp{Q#>Cf-0L)M1>ywAPpa5NS zW9B|gkO9zqN1sr-wcg5uO~=k1PW$g4p;UeNp+!X4fDRz=VhnYJS+BUVaiw>!R}+45 zo>f(K4)vAozBhP$Tv{nG{`VhfVQF!Ea6rf)IY_G$lK*#=3smsy!brfOP5U|tNZJtN z$B@C|jzH%(3CImm*e%GHjyzFh5hH%zheN4e;GhWeCeiJ8#!av4R{(o&)qOAPXD^>> z!09EBZu$f7_Ir?o5!$L&2pZpw$kd5-R&0N8_kBm1?bYGxyx$H5$>58xA}nn8F#pgd zzNiUVTOOPIc_Y5>4;lYniwClH`hdea@HtB#b{c07wl`#un9+!(jUM^5*OWV@Kijbu z1wJmTR}2|m(RtM10=6$$3s$DOhMS0JDs z4}k72Vd_K!*qrnS@R4U;I?oxSzyR#0(lR^XfpT(*u#z0Ab-=+qSEmZ*%ZFJo6p}&YyWQ1q&d<1-^F(*kmg5VB}==qFR6O@Wtfhmm3N00nFBOe$D!F=-q`a$?(yOkJ#E2`nY~Q7AQug zzHRgv8;W#$wm;mLIQS!MUa?%e7ra&nXi%v!mBY+h-B*9CK^#3f@mML`Jp7VRk4%>< z5z*3NdXocJ?!o(dbyX1E$D-z4F8n31u=lDgr?$cwx z&egrUc1MZ*+CiAAiB`RTwbxL0qj%J9T)uG=O#fJUYwv>cE%+VuF2k;h+n4+4+s($x z{Y#{cBe-$@!Bpv$P>;vIior0_-+t}Rp7=9M&>Sz9I>SfC`0?)7%NnFVuW%l`#*Koy z_sOrAGwrf&@c=_6o*p1oe{|k`H4P-lx+$Y<{vMmy-0&Ete+Nh&V$i>ajslnFJPdho z;HcF*QVudI8PQ*~DbFiUnZLA?54j2Ro4rH9+P{^8D$1ejm)HJBa|>#_Fse!Ui4hx@ zyTnyShCAy~O=FgacB7Fn)9+=jmSi1yxZ}7FLL>vbP0j=J@9Bu%#q^Xr8^VU}U%vTq zED;BAiuAkNO&DwTcM;10Dl9cLy=CXEtrGVi-6wF=>4@+^-iJ96CTs(|p@Fbh$9Fs4_LJVR&i>G7w zl8;vlWs2>=nsc+Sj|?{jn5fWi$`R?!tatmo3@B5NGCQLzo@&OfQQknjr76!18V-W*CCc$^*o&=_3K}9Bd!BM(gFE>FmLmypS;8ZDK^78&SM|juKX45 zTvTLoNdu3@yt6F{MJ&R@n)FONZNKl6+M0Iv>-n}A(x=tF&SY>vZd$o&wxeqb?@Ap( zH|g8>1W)GZken_;Wa&f9n&R{%UH^EBqVL{p6Ag}q)owJikK6N{XA9z-INP{y=N+|d zyX`d;%O>ffpTmqB^qhgu5qJ->`z6}|pAlD242T)fa%}AflU~-&)dZCfp7%KU_Gg)P zTgJh=C@;Bk6xU$53iTUxLu)bgq)&W<_) z4HH)saM$GJyCcjJgETfomFX}%R+`Hwb*f1o1n<#U`Zn(?PG}iN+bw3HJ=%BJ7EiKT zjQsFVhYrcCNo#ez{$SeC{JpteH@qRy4k!M36R$f(=gvv}JHLiR+(O$1EX7AJS$mI) z>gQ*t&kD3851p&AE#0!YdFOputx{}4kuwC4zGEG)9JG+76wZ z0U8kN%Ca8B-rm$}EIHyk{Xr!v=*NNercD1siN~dxfj-kn#_s~?*_I?{U(cQP2PCif z*EOGu1|#;H5%m`o?~aA0g?9-0ayTaoM@!)|Zcn_f9Q7Mq(Rx<5&y^K?xJ;jh?9sGG zoR=Zm;mD!5dH0j^QYQSASGJ#*BY&?`mlqT7G5u0-V5@rMO#Tv91qavks3h}TYW61u z*WUffdXP*w%K3#qM2JBX!#tRON7`G~(yV)<`Affqu#t_JCCe|oS36Pd{uY|u1sUrA zJf`-r9CfGj*}LlS&)%ohd>?KB&(=pNl5D}w;I%~-QV1a;-~2?S0{0T+qVwj()qL#L z4}RZeBCABz?!0>FSvVI#&Si5PM*_Z=@zbEJ$0vhqQ_*DTGB&aVlEO=}p47`g+KHwT z49lC;KAcb4T=G)!*cVFUp;8O+n0i51yO&uh|JWuBWirzHq8b10 zzf0BeNIma3v_W5aZo6^kluGhG+}w3Ef8beIPqq(^c_L%o=p0+u)sL+n+j@cW6k?t2 z#O|n`Cp@&xVjKL}P*6pYhM`Q8S@dhSMi87PdU*l-?p^hqHYJxX2KZMXi;MQKm9x+B zog7Vmc&fa}PUu}m>$?XlBxz?7?P$t$Vo&I!kG!5Kna2LRQ4^|c-o?tqS%p)eQ0j>( ztyt7g^@|AE@*l&I~AmEBzk8W-CLQOT2u`eq(P=H53TGRz@U+F@n3Z)nNevkhX# z7fqwrqZYeb2@yBmVoOr$oU)xKUe*yq)%>}kIcdv>JG~RVp51uNKPAid z9M(I(jrF&tw4_EuYca~xs{0!UOFsfjlG2tu2!f0IWpcGEu(Vcu|EOu-+HN+!LHEHz zKzbvi?w4A*0oPwu^vu4&-fk5gI91<8|u5+JK zgS?Zd2wI2x1Cy1__42XFnTWIW`PQPDA{O+mymiyy9(=eWE13$IRrkfoJUEo(JPyB& z&K_KK)YGlpE+D#rjCi}C(6GiIec765q?njb+N~=2Ua0i!&px#L{%iqGP=9KWhQU?v z#GxC?x6)S1+vVBlqe+a18atYmTo@I;=I$S3*K+Q(`l|x}hW(mns2oMywg&l+E92oc zP}K(p?Bv1vzZ_N5U^HBUqta`zlfP#*k2Jw~?z+#wOW0(vC~lN|jM!l8_#Q2|)8>IV z5mEAr})Kh3(4VaTp*5ezt^LtH>bYWAud$!kw<9 zooB9~v-Ya1d`)3G-8-2_*!yWxmUpm~0ZNN5T@7?U}LhLraAs-uJYd|0r7VZ#~C} z{)TJ788m-wf5$dU)6O%xo%>4xI0lzohOXi#g~2n-AcOZTZy|)-ia}K`cilKUh7stL z>MTgfo8wB5jj(Th-F!X2yNG6@`sG+0>jM;}TYsjM-P_oR9Iue?e4!=dim=U9YDq`A zDiWn~&yIKqmV``pUMu$$(m7{f@y{KZ!62Irpr+=&8r?gMV3Tu10rt&&U7|TQ5w~ef3rw6 zA5J?&&+rX372cd*&lhv{GCE)~DnjBviE<%6+S4s+U_O7&>M7&i4X+yK``53{K~RuQ7j)qTVf>gxsg0#1Ws`Ka4$12| zBhv^PjCgU1DHOQX7ZpWEZguc48!>zgft#gp#$-1<0hh z0#l18o26!2E|}bzL#uc+FP5C2Y4yCEo`Tq5r7H1=x@yM?qh zhg*D=sI)T+b7T5W^N-@*s@#iQb4h9R|^O_BFI}Rr#6Xe$7m?z59C> zJY3cZJh3QFE^kgXzZrn_%4K(+M#EMPGi?%=EE+$wrYp;a-o3KW)E@>36!9JeS{`zl zn(-G8-$SAX;1~`V<^Tt;j6zY%M7r@xJysEu%$nPU)bM2Td`34MRMmf`o^Gy#;Q$KTWc4#@>|*u99;Vu%h+5B^4*&X z2eK3T)u`&w65?BSQAv(izmX9hv&AFbckO)J9qy|(86y4!5$#Z7A$a=diyI~wldi4o zM8_OSnbg$dtNg*Z=HtT_(_AMEY7h9eFm@u(~RWD|ec$ zW|b)oJG~@N&U6hQG1h#h?#7Mz#ZOY!*`=pw>%dT`-MM3V;kGXzC^j>-_S&o+OsJ%K zr?N*Ao~TD&U6C1c!ILKp_F4z|oyPFE9=3uhmc<1ISF#0t_5q3Coqu8X`SwI5H+{4@z1^Ab8X1EN_^2*F?kF_C)(E8BkR@N$?A_lWSrCh5W8(nc4V6>Z@ShBB@_i~7&_Jp??3 zgD$3dHU?1IyB@>n%femZz(D9}0-Us~)YYs;gQ5EqqL#YLRmPhopRm%wP3@!_p9c@7 zRFKrSkeeRjDx!FS7?0E;MH|yQIXPp&IqWA(IEj9sf@B z+lE5)e;rHF$9?OSO*R;?L}sa@atWC*Oc8D)9yxuP4|(3 zHRj}w-!$&Yk(){U)>cZ!>ABzT2c^e)7XzIQo$$sUF(Sfpzwc5yW)yFR)PCNW#3ga$ zErPG{W)#>nb$a2%jXgIqcqUFT?Nr%}olPzooc5M&Q@|YDj{rvcD{|d}~yAT+^>d;ev}dY}Atf@=FO8S3R9Gby0}{ zlqZfLT4}Lk*GPUGu4(tv8S0i^G4dwa=09*+nOtwFY>EJIy8gDk^f5@TmDmXI||NOU!%vSzGVN0ysi7)eTHiMW!oCHwMw-RgIK=lt$D z_n!0q^StN#ywCSM=RD6p-|zc*vsSC1d@TpT*VISo`AABng+sm#^=>-kW-{R&S;6;k zDZWEjNxP>LOI)ZdII>!x%<=~TWwmWnQs;xOybo_L43KnQB{!x{U1W?NB9LlljsSla za~m*|8|Kc0onMfKphNQBi-zQ{<8Wv$hw4z6>dE%J}+If0yW6k<~w`LDMlTNEy^W^q9Jm%FUag zy1N(hIFEVRi7>FeNRDecJppZTLquU3S^Nl45*qe-cR))YZHtr zI!Q$E?I=xb!x6doQ*u!hu6-$?C_GGaKz`EgLC%ns!i;6aOu8(`ex={Y`D>=_E4AW_ zb>=W$@{CXq>N-DOBf$H$TOY{GfALaw{=%5i3$cBCE`2?Z>#%X8r=@eoUd-X_XC%i5ky{%e=3)k8QPR20TvwEx$N6H$z6eN;ehM%^eCHjLr%N@} z4wSNgzbX=Qik$qWS0vwY;&jc^EtUzbz>V?auY<$5Nt)5DCaKT9F%K@`OHh5g#m&hB z%`73QRKh#W@PM@e*X3#P4xIy#>bMo~9ZI!oKDmc`=-# zRwtT+7|Kxo%F~xu?Y(OiZ2H{{vk)P1#!KuTMSi(6SDRYj+)P)>nA`+EA|UC_WcJK7 z+U(K3r=})JWaOiE7Tyw!YmdeR;c)SA>2ptA_tes)6CI;ewbr3m6I?;`mO;6uV-kKx zxm?SKp5jN?NL_{5eXyF1=8nzcZ*NbH-})k0@~OgT%zOUop1r+oxzoe03b3}FK>tW@ zT|Pm@aNx_FRGE(9#s?RKV7fT7X#rDE6RiM8xzlhZcL=4EXVe}!VLG#aBdhr6NmN$q z=+5(0cXsTvq4d2H|0#Ev;%V=_BN<8K=XC2|&!pcRgFV3_CNYh}JPCnZ{PYa*PMqNA z2_}}~CZ0!+eAp_tb_?EPfi@UP|4l9RK&AOrO9e0(Cz2yz*GK@QjTylb0DBNn2pkIN zHkyFE1E4ox3E=gwAzxZph`!9*{--!)$X9_;^fItl`OK=MGk`Kbf_Z&mq+4g}yp zrhb41WB`T%nh(as#}`n1{;Mf~Q7GuY7K`%D-g~@L2ZgR%^jY69X|$M-;=QSEY^-sb z>CU6uDl%)#qe`_iNW|tg{hiTm1XctK$1T$P6y=>`kE;uZLvMhhra=*_s`k8%afcj1 zY;1|SwhV2tgA8a0{K(n65`HJkY)lH@_;!D(e5DQl{xr0##I0t7$q@R+YjjiaYI$U8P#}Wa1o?>a?Wg`|Kueu1gFu6O#xngED z%w)9`*rJ~hQsm0f)s~#)<66~O_h68fpmXQU!-+iIai2_Vu?*?3Qyx5$&z63ne{4{! zH$!T`9a2SdWynDla(R_XN4^5vh-IGeo|yM}Gcn7ifYPqltvi(>C8F7+hrK=&k&|Ei z1|vPPzz}jmSZRC88mm)Os98WEjJbUk_U+Duzq1NoZOKViOEzRqlg4Cs1{dku6w#p2uFz3^qOkuBiA9!E0IiFPwU%qp5VKMhia^Y@7{{2L|kAKS11PTqi1=hK~ zOp(?YZP@p<$L3ou(_gVYEhV9er`Q{AYupVUX}yC11@dlFJ*Nsz-XHq`$aTs4V>X~tTk={bDtvcw4$I(VIyRc2=_L@ZKe84uO1~>ka=)>B4mwo@k zzOcpJo+kT4`-S$_LXNklBUCQ%bSTG7G4*{{$MDYlL7RqyvOeBCD!S3yRjxKO&;khq zpIHsE{H#icBpi-&h}CgpJ%PR#bFMyg9OrK(pj?KsWGx7|FUHIdG;}TrN|aPsD!O;$ z)pwcM%7~SJa~B-=P`~bipFWle;VPTlB@ZXUUuG3d5x}ZUU4jT;7|?8C0k(#L;b7PS zVCCuQ2Zo`5`6dV9S3SY7pWM|YEwHr;8V!ddps0%qFeFq1sila}lvmV5pwSxgS}1KO z26X}a&mq7nKNJ(--2HngjPH3RM>v>)X>eQO5o%#l20)2pefho$P5Nx8N+J+dm F{{ZZnw|D>m literal 0 HcmV?d00001 diff --git a/vektor_add.png b/vektor_add.png new file mode 100644 index 0000000000000000000000000000000000000000..3092592c5c58dd8d6f31a264599b856625966e3e GIT binary patch literal 14041 zcmeIYcUY56(>EMIKoCSkPy_^#CKyGKB1KRs(whMx^eQ0%>AeUlDos&BFE&bI=sD?K zLAsPcLIk8s3BA|%#Or$Q_kND!`~Ls__&5;voSmJSot-Ve*?pz2tIo`Lkr4ucFl#(e zF@!*900@NY%SjrLva^!{elQ3*-@mW#Y-b07Jb0Cm;H3Y~^nA*KatHPEPnDNfd+b~d_kv_CI1F@X>Y0vxYS(6oJ8E1U1+A{SYrF9i^PLtU?2HiZtGisMk6s*kF1>yz8@^7={ejHZ^LQ9woWvKO4D>Qw zN^D<0C!qdaNF~H*`6ywZ=Zm^yPJxQ6N1M=Hq?fkbTIgvh3GrJetejSw=e6Q4s~v@Q zJE>aLOa?%Ro)Esh+JLbHh}R;u@@|ib9;%|?eGo)$aar<2@=-u;0yFc;FzP?bbRyKS zEC#Qqtl~82dJb90`QKDQch3+Z+kA8a)KovHE3D~7Agb29vL`Xh(8my+EcP_I^xq2Q z)cFzQ-`6kD#XUWv9iFIsV&p09$?(E6oFDH>ygB>%^sKVl8Lr|N+1d70O?0)W5LlE21T8E@&(WE}Zc>yLU|T)kUk;%~0y;cfYCjeY97;r0BFSc4ecpYc3nyeBqx(I$HN z#RCD%na)?1-yV(o*wU_?TcLAL+kUDd==`qy^BF@r=Nq%Kvl6qHXPJ|=2l&YG5v{Y6 zHIqWCuvMegz?&&a85i`f-9x56!as^6z9EV+W_;8g)0fuw5Se-}`Ck6Lse5(#3t1Bd z?I5fle*5-{!OCrhlxH8FMXG#MDN-rsP_JzdR_x}7*@dWfnd}q8Of1r+! zaqM-ct1XFQ@8zLe4=$kx(Oc-zYoXe;Rw24~4H`5qt9~#X!!&;7zu#kgQ@2Qa<>Pqt zS)Eq1tHycSv+=#BvIX8XX3^sZs!pr)<}# z#qvw{yLE2p6&Nig)TV?K9)=v;Iq0SnqGO-~eZ`#j;`$5!7sD??xtzIHVlXj_1wsWr z<~1nq!MVX^x#qXc>e0MOKed19_@u5U1xZLrvL^v4T}gS#&r=9VF~ze;J)fIIzET@n2)%$mW>k$blXf_v53>kU*MclNnn@woT`=gx9bnSbD#@qQ^vJ-cM*UQfF^@ z+`^&$_T8&K$DH=A$4(|Q2VI{OXfI_Beq*ahszAEWdJ9(UmK#^x@$BG$tTzB5|pK+OikM9xn z`ffB8v}BI+j*m_%@mllhU*u!zXZdy3PyT_lh;**l1+E3&Ul$b0x@?9Uyx(0Gx=efd z%Dm}($>8WOzN*VMP0wTA$JlUnKl^x}=3eUk^Gynkb4}BY{$o;O{C5&VUmi&`N`Jg& zE7U7me9J?$O%!trAvYwttGuoqt)uPVfxIRIh;DkPd77hs1y!r>uWWyL7WNEKF}Hm@ zULk-m3^H^pw)OB?wSKLudH1zAfq%mq^WeAWW9^9EfgJBIeThon51BfnEjTBV2a*ZN zOC|dyUG`e`!VX(*y(6VgeGg;py7W>FQg>1VJrX>9Cu7~lka=WA6!Yj%iHszl_s8K%7Y`q;O!SWA*3bxM3#xD0Yzk7iNNy!ZDtRi-y0hP?wrF@9 zI*J>M%jjh;Rhzn+TL!*-A~Nx&uo3qWYl!o(nzDsy6Q1BLyx}oHof#=RO{|fTvBXQx zI9M(ebKrMt^G}3aPGxLB%+ z%2cYB*>7|-I{DpY;iW_5k*5jP)y0DA6YkGB*#!5w?>9cwMW^{F4tu@`&ffUCOG@!E z3$&r{FUq^$&)Ii%fpPAl!i-0L4!OAMz@)}1F4N?WRq)-_d#$RC-}j@m5e~`7Qq~HMQ3cq5t|x23e^zv&mQw6Ypks>C6@miaC- zQSYjbln$3pW~O^u#h&eORBPhZ8|NKQ9lqZ#nNFC-mV}ZH2{#ze>C|#mTkckE$8@Al zxW$ZacKCNG1}AR2+SD%BbnLP55_xy;&;_NL{V@A>-8iUsxBq~&u|_l;@9kB(ckNB> zJ5Qa5;K7N{?t!5W1QH+wfrLGSKz2b=*dGYQTO0zJvxY$Ak|2=tPtqz46u{#aL|^-% z>e0~=$OHb={nyWbC}07s{?G4!fBwVs59Ocof3y9E{txjVhE)-f4PM@PMMY4g0VE$( zC?O%i!NHN8oz2I`hs9z+%8-XgeSJMxSP>QF;MfKWNl8geOiU+EoUpUAV`XL4)6?5! zWt}!KSQiigYeD8UK|uq9>1!uRZM3%w3JRvRv?gFM2FNBOWFsA7D-CJ0hon7*BwvP% z{8v~0W9*SIgd`1V2dl&(-5roye|i36K14%f=Je@ZUfzv}i2na>E-ASf7xz;@U_B|R z%fw`YhiB8n!-JQXHzFc}o}OMpV#&^K6odKE9}zL5q0ya?aR2_Sh{!4%+fG5jcO|9y z($dn(%F2q03b1z=3mLfXS^r3 z>PE}9riTYdtL7wq!G_7hr7lZ7*)LZd58!o6qnRoli~N6nmoKJb|+Az?Cv2K5d`M>3}bwyIWzru0pum-dsAq@9)nge;tWTR1)86;e>v2*!Y zK}&9gZCt#F35TjlR88y1gqi;|S!7*jhM2@d>7IH&o zg$`QZ(DK$UPOw4;Mq;lCEu0G*4mGNmetV$9^NG`m8qlVK?_yN#$qJ7bTq)l&7tAY5 zOZL?nPau=2fpyraA3)FYR6yc*cS=TC-WO4#1TAtF%MpiCx^QO7E=Fm1Q=t?nrh;dO zQAFrd6RcP3U*cv^vw4jF$bD`{W_iE35L@UPVD{nxtR4-u*0RDsLEf-fKI+@5KGl5ks;Mm3ZX)u(%Ph@y z+-vmzbUo_F=J-pLQOiB-r?7v_V z*E{j3FU6y7BX~BZs-Gt8|2ncwx}!G70b3($-F~j{OM#gJARj~VQ!XCxwEtJuCGv|I z$_w6w1w=I;Er2}k{&%}7`4qfwE4f$d((V5dA4h30E^S1N$`c1o|CJuq0&wP`0?2Y? zaKuj?8+M7T`J@T(f0E^pTBA~rzIyDLFr?Vt`IPhPOG5t{b}hC-!kdf<*}$6bamNa+ zUF=}|Km>+NF}5hHEc;^swqr-4zG^lNxTjlJZQpJ8hNmw?K7|Iu3h_mv4CDa$JMxRy zd`^L}(lF4BIfs;|tmLg!&R6PA(=?!KMTtX?62fst=|Mq%Dk&Xc7|&wEDVin}x9pJQ zaMWPB-`BlPirK(Fy!l>)?6R8VRR>0(_F>tjP=!ZcXr^PyK3}lXiZ__A(~?DrUG&I2 zJ1D%HoWgTbvjNB`4`Kq`>(O!?B^%Wd(;=(v0y1F(^b;&wKg(jMf&QWtT&C8m=fCq> z1ST{+xC_6;Qjm&nWjEusIykma>bJKlDH`!EMdsQ;!Bv^_%1ZuxX|`-MDN1iPd0MT? zt_Jh1OewAY*;%JC(ot*>ItiC!}1K(9%oiC`mF;PFvMNRKf%b(n>_a|(DEp(B@d){C5S;lt%)8(CmS7T4M z+ueft3aSrH-i>;6doIcc=Ff4tPjqRXP?C?USe$UnI9g?M|5f&lw|b*vw;DBv0+nt~ zK2`VR@w?^!o6<`kU$;2_nZ;gFX@};v73+?0h63Nww^x>Lmv?IHWLrc1Cb&kovt^G~ zlv-<#gl?ZNK6p1Hxt4QSx;NY1ekW+8=BWB8EoCQwYr*8$31g+Do@s&B5K_qad}pUQz4SZ! z&4_|;!Q`F4IuiDJ>Cajn?jL#FIjHYv>sH9xe*J6hk7872=1(e;aIO0$Ep@?5B3q{1 z8O6FA+IRP64y(7Q8?_8K1QA+|z(lEqFSAK}p50W!WSw}yX4J@Uo->vj`8U#BxIUjl z&NpNgU3Z1NZP5g*6rwh@!lR6Qdx|Jf7@QhNKZBd!tVb(s7S(uc41FDvp&cGUHR3-H z;kQ3+Y&M^ez%80M(rX7HhTTBmK43rq(au&$zL?&6ia$}|#73pAb z!{T3{a8egq+$DJ(1WvSOr7$DeA)3Z1@?x}-`5d1V<{ zZjEq;9FDdinn;WSTJ<`0E-aF~j|IuM%X;3OfX{usMqYRHd0%jnpi8HSNTIrwncST1 z#kS@6OU+~woT1oO>5^og87-mnpZ2+*Sv3tgaqEbl)x-XWrJH%f$ zi$_3J145k}r7h=pka;Dx$V8cvPxK>?wfh&<;QnA`JaU3H!&)ny-BxU%Blev&`DHCN za6%(PAkNh~0_tu29QQ<0Uh^LAd_g7+u*;Tr(9TNkDNX=ez^uhc9WOL6iZAQvfFZU# zRH(yxU5`lvTJE`%*l@>-SN+l-k7BaNB5;e}5P?1P6L*jG+$(`OJ2u@?vlvoS;J(d7 zM07nut&jOR`xbuDbthq@N^CB^J7o~ldRu~s(7lIRZr$eQM7A1f18v|?sjaTM+Xclk z0RfUV05zQiDpN>;RB#K^ui&R$8g9VR z$GzUz2%Sp{Urlmo@9$`)f-9P4A6Ldg?IgMAk$C$&vqHhR%fM2=Wv63;w|&JifeHwb z+~W^-1nSmVt+AJ>5e;aCU&z*gl9=^Cd}|o$@a3`0C&gbDI;ADl)C6gOiYuQ%xlPUJ z&5!O^ihALW_0n$N`op3AkBDI8+z8pyD&=_Wcgc)g`o}@+*xdWw(zs-TIZPW$oQ}=~ zm9jv|Uq`-wh{CI8h7-(o@wO>~-WzN_#F^aMa`JhMzEE-{jox?680(?Yze~ZA(V(w*94oXi^0bNOU$sFw1jY+$K)|nDOLPM z>Mvz6qvwLSiK1$T$6PFYq|5q_(>zacX7dczdNyL(;}xn zf<9=yLib=xRDXvkilK#9h+sh_Cn5ZgXhqM%VR&mXcJJdz5e$3D0qsJN+~UhWaP+i@H-w!6!dtPRJ(5)4Dn_qmpA}bqj&eO#e&Ng#uxQ=R zP7CZDdnibGpIjLMHJKzKj>pQswaTi4bR2})4@w9hIFK54S;;Xpfc9GltSXe)`@BL% zp2r#3lf#5livJj#0&d+L>}Y=LKql7Yeh?*IeKTU0N5gQz0{FMrog{On@C>cQD$Z-qw zl2aHfND&U-a*XN(@{FKFN7a&{@xq!r)izlek8hF6?5UJ4v>M(zm30^q)wD@92N?6h zD=zDQcjPKRwyE!v18llw44KNClMPhDUmxHHYrH7ZH zx9xAksqxRP+oh~!c;N&FMKEBcfk@Zz--f_BL{$CeZqX}@VXNeEVhO^((vR91(uryuta+^ut0&%=DTfPuGu{)`|8B?CdFhct8#R{$qfjdJgPACx zo+DgaAlB6P30qt7sa;acCg(uqf5FPV|(=_|YhEH6?$PL!P z>vx@|^*P{%con4H_;imGN5`3EW)T2rxjPZy-{B*x(79nQNjjVFY%UI%B5wGVkkADP zL2|5-q5{%4xWM};Vs7l#FD9TA;Y_?V9DPGA{d8o5x=g->$vk;PmN|6j4&^g48@{qMB0ojo{pZlPpQClSz?W5xpiY6blGZsMZciL7+BrHdY^L$ z+(9h&y=cPzg;_Ke8S@J8T^tSLcjG6}sC1~Fv*nu@B)sP!0}XfC3#wYwPJRgVgLcHa zlI(%lnZuSDZR1b3d4vYDlka(6*+%w$=p4kS+qIW?E59W!F1^M%^epdc!l3r^+-gT# zHFUlqK{4%cxCg$p37YSSj}3K5O0IzYc4dxizvwnLlVaTt+}C?cG`_ybh;wjH9OpLQ zBl--je9uMC)A16j@Lz)A0r*nn4JUl;jo=n5Ma~&NzxW?%o}(ev<~m*ZlxNWS(~8e+ z=c@>1=dMfrJ$?{|QR zN2B%L>HYK_MN|4(ZJU~o^CAtKk3B}xN?hhm4n%3V#@M4#KGHH<>b$w99|3U`k-+>a zbbvJ)8f9h(yc<{zSGNH(YD+f{%`?XKe2PGlOvx~fm1+{@XQyfw6?BwPNOZqO2l z%qMFoiZ`Lvp;yTo^L__&NZ88F)`^v9|4M*vE7gJlkcT%stc@BO=z5MzZ|f5LPT;0E zkh}g2brm`oYI%)rn*D6s%_&>)kenDh{|>{5OsE3X%DkikC#SJEUrHdzytP%h!i>JUUEbUpYJ$45$QA6rY`fjG6978DuD{k|aCx95ilfG*5hHn0r z%LbuU2GzBwmf33|5JB={xeJ_}dMDnxJqP`avN5)jVBI#{<6dq@iJ7R_)S0IHiGN)B zy;Y|oAEha|XLtoGnd(G-G~l;6(LCVhSmpr}w3pAVjQAdxRpCZvHY3H(8-MCJ|fFdvD2}cDN zYfsYTj>89AGIp;sodGy(Et)?nxO3^%LWhrg3-UJMtc6Cc#|FZFqv2hD{^wt2hGnj4 z+jF|KRRF1mt}R+y3=<5x!Q=6&NfV zt~lG^$R za)+py$LxcSs{;1+5a6t=x<&=}!K*q223^Dz2H5!pi5;+>y`QDoVyuf2C-N^2Nng)} zL51NV$2@2A6ge%mNyzrY3fPVLQ5 zm5|TwvqU;q+WuYP7R&YDegYmw_$as<5XY$x_X85(CPuCY7;tOiC2LwuGWp9R99aN6 zAeEjr%?#E$pNu(ju%jrG9y51~(s> zM_{(D1`TRiZjWCrzOg$WI^ou9(wRDwp;)#IvpRfjvX5JinEAE#I&mg9z$$hoz==ue zN^PugUz`GKOR&~{1H8NZZ2D!T!wc{RSbJb*z-WO^a&ULmsKc)BJ+J9sb9f+oXo%ez zwI*GHfJr&9o53wwM~57 z@FJZhFZG-R+<$-+8gkD9RiR*~J+}mr?t^(>`3Yo;XGlF-;uVR;TB|0z=m04!xlxZ6 zZ@sM~=+s{59kzjFTXShZUpJE6(Ck1v&qK&0A*b&VP}A(0L39Fi^t2+ngd#jxT=AoyRty$kY(+lv`R>!kSy$P~TeZFQYJLMHxb>Ka>E8l?wRyFKNJ;|MsvU$gnOF)^ z#{{2_YD2h9S-W`DnSz;_DP-TkV=!tb6 zOhvJjaPTBErzv~-_ID@|p|g2M$*0I7sOJJwO3+hJv5=5VTjfb=^4U?fDVG#E-_B z@djfP^nzSX8`2?C`6=q~8hB8wEJhY=CpcimdoLi@oLt_T6%yV%AWYuj#vj-fc4nsI zXu;FB9vWkD7nlQqgzQ3vMVS zZl5vM3pQdHpd86y{FE9_xaD)>Vy@^#7a}7TDgsaW&e33elewD>OjY~y=L2ELSq}IK zIR4qh8{e&D>}xOuaTXEPjP}y8D}=R;lV~2o1a0ZzoOo4Rt=jCHM2yP4zwirXL-auM zKmf+K;5oAGtr7erU=F7b!v%fr562+{2q{kO<@Z^Ln(Dex5QiD#Oo0yh^)MVV#RK#P zv=_l#JT-cf1?k}FZURC%QB_OaWgv9sDjV0>Q=C^&*;$ZFkP)F%CD(w@H}TTXdip zNM(`RgK|ueOz=4@q61M# z$n#-^H-e#umKzVdcsue@E{u?zV2y>Lgy2I`F(A1y?4m#YEm0UD1!j#kL5ae5|B^q3 zd30aW$6#c{>Wxc={DEs=j6uCmP|bp1m9q!ulL93VP=U&BDyI;_Q30h`ox-VKAO_02 za^gXmS)oo$2>vE~kq5-@a{OVXV0xkSOfEC=A`uL|yep6gbs!7F^Px{UBTlwg6hN;- zvTA+s*7Cduh)&9JRIpO@58^nGGapTHqytCL&U<0Ipe72k6eCr0yiCy>F(ehg0o|ZV z1mmz3^qJ{5ki5B1>%VQm>5q`lmFbyLW;CBCO^M7bmjB2-f!Fwv% zHU#bQa+MB~gs4uukx9m$&G7?gg61zU&g8M#H2g`5eEJD;&+V`uja|W2Y{*oK{S4l$ zkogMEIOLyi<}+Y!h?zgn*!lC#<9gaNHD-mlA9=7#V3x$kIGz4m76;Oye>(Xm&G9Eq zzY~c1KO)w2!GHr*lmXwsKz)FF0S1wa6QREriXZANvB)>>t2PBE8R8;eqe09mOmB`j zGBJ-(ra%koV3!O_inp%P$Bq26pjo%SXCTue@CDSgpbA=eb~MQ`PtX)x(Ed7zvq;AT zglPQ7Es@D*OLPphD*k?XpUCy^QGtz|3!|i&jZ4LZ9t`Rz3>HWlZp?=^o!}eCxTN>r zaI01d5|gR6&@FR^O{aw(jY{fE>HhFBgEpl!^KOT|n%Uiod3f-mEX7*O98b>A3HG0O z1<@Cmc-@D3m>@rs>4$!bai<0}@Csn?QC^!+DqW>$T~CUnDE^!b%ol3_uB`q3vOSSfU`O@&VC8*; zNd)T4G~(I(A&nJh*j@6V+S&I4CrAq9(%}SYzu|p#TtP=kBtWJx*eI&`KBN+ zQ&MQLf?)&hzN?bnU2Q(PmF1&KR7*Edd=hvxf5pfVOz-dHoW38jS9TlIF%6G?crb8u zP#6rW>r8)rLk8)oQ;HXB0t{KKunfPtl%+-w<=KjPchXscf2y9r2etTy3@Yu-JRJ)C zuYC-?WMdgFLjNjSNP+{B$LbOFiO-ZGv)_p1D4 z{40NJu7U%io65uNC`0pD6~vsCKf|HH*PO`t%tBUlWZGH8eeePcJYnGPNY%0;OD6vO z{Z68cSx>iHrzSsDE49|*bs=RlZBvmunCvfA-vZ~X7AZTnmj<4lWV3g;m72TDtcD30 zK9X!emt)@5UR!FWk1mul+}NiN=~pJmIudQ6SLLy`46@l_IK<`&U&!&a1@ArAi@jYw z{=GW`6E8JL7KzGnREWiBQPUV z3P>Jb!Q#y1po6S9MnL*_cKor2d#Xkz{d0$XRgRR;0N|}%T#he-)iezLz2rQ;vjZiW zBM0fjBRFTU;kX!B`;Sc-?i%?w44-GJ=bU@ozpc4r@IEf<^1i28R6`F&Mz9$nkCx1} zKAb=XqM92wvW!nWwkRJh5a!amGcN106B@g0grhs!6|~=*Y_XUwTg{sDu{v-c#4TP8 z4#aVM74^6fI$a)KcW8z;3ncVyIcO2}2_kVYk6_^q^x27^>jX*O>bD0rz0pnJzl$5xdEmhf6P%nqrhTLPJ0B zjz1i{r|f;y{oF&ofTIqx%zGZH@pXzgwa-Oxsfc?<8OiG0IP2>~*AC;%bmevhBAz_e zbpPs)(HtP3wyFPV~jhQ{*TpJ*T~rh;K^&z0<-dGl>w!Hk&&+uZ2m zLGd*tcsgyF_>+vAg5yIwdMfr-d$*57bo)Q$Gaf<-XUfgD=Jga?*C^H+l1f6OwolV|Y!oTfQO?b(dxw{~2kDr2jXVX?0?7v*!mY7K!aLGi4k@n7 zakp*T*BMzpUNQ{QnET0;B~eIGJNkT?Y+ZJb6m@>gw*K8|ob@1>zvMmIb|I2hM_<3{ z3T(vGpot1?`+4d|@vP*4)Qtt(_lAYc`~7wR&G(VSP@iDgLwDO8JA9#Gy|k>3r5k&* zmAUov=FRdV9;-e|QOrBW>qh;R?xR4v;%Ul$YO>pD0V4_EFi?}CM*gPktxIF}j< zv<>~r$BWVtZQgLoDP~$4|*gBa6I1x1u z?{+4n%pabxt4Mwyi7Gf)TRHn=zBlo@9NslZL!y5< znUf}hS#ewzEj(87;}x>Eq=b^o+_?7V!5a=a+>l=bA>WI#`6r|KgWr~)m&w~L0snJ# zh{P3DSJmLioA3sa$EpO`r1{n3YCk{S;sT+RPFJ~Ba)|jlTuzWcv^yV<+ zbyEj$Ua{(oepG>LFyj5WnO`P_4i8Xs{4tGLlfPf!jBuLF-WOFQCujgsv9ZZ0EBtp- zJ?{(0k9QBEg|QaC5<gzlChRbp`|;+s?I7hNQBIUiVO|e^6O*}Z3Pq204OLZL@)aRy$K^;{ zwrJR%(s%H@WvO6AkNsw$_h8n5x6)>m_u|S%#E|50Bw}HU4PLjdQRu)R-S+vk&o8_G ze$#}O19wpHY0ba;-#=jF-}ftj-y7m+9W~IAeuRT{&c)aHXJ{x0gvtfzXAWB@xVm~vbXmC^8>)wd?&+?e+QZ;`5vkw11Fx{ce literal 0 HcmV?d00001 diff --git a/vektor_addition.pdf b/vektor_addition.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a19049f09d635631e854bb4009c0a86250e70c68 GIT binary patch literal 19207 zcma&NQ;aT7@UAt+8!;*4Vaf+qP}nwr$URGqZpDm+R)il#MIc%#1w{~AI8bq(bUie#(i@~Q#Njk9jWI_{l5J#Q7Q|d7vdlM^Qm(H zeqc7cgx5NJyw0ZH=hhcxL|!VL-Hxzwe^;Vd+>i&$(80Xgp?bmaLw+dDK_3d~I2cw$ zh>PB*!N}6oK@`v>rP=vkNj#z-T~a3gvQq)cbB*84ud*~a?wpv5(K>b+DaTK7rqU0$ z1v*LkrCg&ba`pNvG(<2@#sykpUX4Y{cZhCmrA^U+5~i z+DHv)s|}A>s^ECjT3D*bfs=E1l$aB%7P<71Onb){UrHMET^H7YJe58UN83BxTaNJk*M} zv4?%Mv{sg~kKc4(&fy}1lae<|3YjX8fpJ36jRct(CTB>E=${>gOJv6uoli^QT}xB; z`I5{Yw#LSi)Z1!Qm~?u!XT{N#og$ar78 z+14=0aHO~J_;P>$86zx=j?HlgkTO#m;|oN-AwHiD9m$6g;9t=*=jUH6Pd8)ps9MS6 zB;y)g?&v0`?|&iHDo^IeqQoVOEel$(xrQl;G#L93kQtXOxrQymTvA@JNP$}BH)D4R zM_^iQ?WB2Jw?rFKJTaFanapy+mj@`fy2d51EYACMl%Y${@N}g8#iQa$#8xD!SlQ%L z3Mh7aGtC>-I|RtRnktA-<|JS%{O=t+C7JckbACDYLfi+0GW2DKNAqlm<^KQufW*{Q z&IBXuXMyVD)RG1XzA@5`kQ=GqK;}~+G6DtAqLI}KY_ANYLk|H0)DjY}oVmyi`Xds{ zEcu2OSIQ1m`tQp|QI5b?H#vr_v%TSiKMwD-2%M`Tqqzw5iYP@oWHmgCDlLJF8i!B8 ze;b+8idBc0Zy*3a)7ThR%kUUh*-IGqjf*C@)cuxQ!6?+Vi9Oy=D6 zAxO$+K?v&~j^H*|3oFp6#|l+>l_pxEbLiQ2jjL2uHWWUUHcJ=eo1EWDD$=W#ZO(cn z3r~|}L3`dApJOiBnqxkwfU|8sw`n*1hR0pwTTGBu!Cv3=7jJ7h=^ZLL4+|B`xKKI2 zDszFcpWkj3M9-T6u>u-1@jBT`m+Z(r1vR>t=N+a!GC!Nz=41rUQj|sDq=R)_tvZn~ zm`qL&7UlFhO>g$)Z#O<=_7?w}K-|wu4`J1RefrEhW>YfX!mR%`=81bO=WzSxvNWtJ zR5pv4ni^d0L`W7{*RZMJikScH^8R`n6AJ*i>-j5Q68&Aa?*0gDH zOQi~5#?=CdIL8u&LZT~}8d5oOgrP*B^h9XktZaWKozrRdPSRvy$n-^UGj*7C$6%?F z6^=zAc9Mmv{=32rLL)*pWutbgFb$?A78zkBDQ8PhA5AgJzO#P4&Q8m)&N+i!1IJg6 z8Fa~G%XE{_P)4c|+*vx&bSCC-)|959g86D~M@&=gqO0pXQLcQsJI6E}*oex0(BZN* zY4tgz7`Z3pg27ec4PC#of;VMm=Js;>018YTGTNz?iL2QqFcgn%tnUnVm1p)I=)SYq#s z7RJ=p!)9`8fZ`tr;)O*Z)o`9cjC=~Xd9ltxCX;PyiR3@nhIjrWIZtmS{(nXxfutpOFaRkC z3XTCq$c*7Mf{1}G{$2ZW!GE)X#UwC6VqZSRq4hK&X)(y)!93mFp@el92PK+&c=HJR zK?7WXFbA3Jn|Zb|?75f)2@XMiSuz>1IQrLt13vH=g*FZO2>)>co!N`^@7H4LObV-O zb7K4R;29K`z%mLB==ue@_<@1}`_V%JVL<#=ZRcH22|=ytPat8!T?7WUdlKo~0J}n& zbM_1Bs$*V7po0nO*f0bjnZu!^Av%N+W)msk?yFxR`FAer0)cTHAYVSFRqo;~FS_-UCKF!o~r4}s*{dj->M^i>^g+js4;+y4Fw zrs&5FE+W7L>I49;CQ!y0wTr8o*7^?m)ZmsEnU$0lP~KS{`vNB?CFK3%;>)1~B}8z+ zfP#ief!iDqeSfQ+AOqi*#{7;gJ2r`c(?;mOMs%0=__}_HfbR%G?ty`Jx$hyOBe6Wsr1-1RB___6j?KlU+y_wgwConHfJX1{Rme}{?aq0H+9pm1FXj2xKf zg%5}KKlc<^-tBHK2W*fLb$@s&LqhhC^N%g#ikgu$WH3ozx8nNCNq7%h-H4JfxY|jtd6J&_K2` zX_=jHfQJAe!MR_?0igUfh9?5?A^gIH_FZ2Gh_$u7*SarrUua(j2KZh}m%w^6}D*`Y6D>b-0FDW|+P38jE@3boo zYhDpIunkppn@z&T6b!F*GNkXg_4aZ~>_>bo(rRW&^kQ#^JBBfZm&B^|Eq82(rO)40 ztzX80kchewpEft~?BB7qmx(gEo)}b1cKUD)bo0PRrVqNIeU82DyzpAlt>F?2@@LBl zH=M*#Z{>xVcLccUrMHGYSm@<9Kkgn;G-%Q_CE_JkdG%75e-K zK*pOnq4VBs+7BTsl038`V^)@hUd}(y1#*$8A6vZ!dVhP|JDwg(?0n(3ZVy$w?S+dVW5}Tix;b9>Oiu4 z-}Gs@`|XWsU-R0P6$xjUPu5URvW1dwdiC0Fa`fzPJdk6)cjBk2q1GJU95mM7X`gf$ zRBYV^(mq$++d3it^8W^WO0p_p_ve0l_pmT?hW>453v4=kGLnDC*XHuArqhe?wcU8I zCH&6fH^IrJ%@zZ1A>IF~?MCCo!P(c81 z8qrJTAFv27j80(qb^_-i1n_>Yl3`O_h9C_OowRvINJB&>Blrq6=XvBQ@RoM*AT?wB zvUbW^__mQzMA~(SdK`YWw4!tfq8L`3>9cUSir!>oxH6yAHf6bKH0cX6#IJI+CTq&T zp2mLRBkJ00vmcrK&W86br>8tv;y3n$dgsS7g&)Dn(eCdyqi@(ggs=K3GSyP`m0h;A zi9T}C)V}#HzO>%Guo;X&ru=;+TZ`Zsn2$}BxlszQlMNG=VR}a1laBlPo5kpaA8&l9 zcEi`br5E;U(p-TMEhbCk!7CC6_@{6tWPIhCqy{uTQOu^v(A1RPcCk5IS#>b$O;P0n zr_)dwOR%@a!9_m-N3>1KHvLvCKqt(#d_I9I_I$HcCf52;b;ogO8AS$to%aSL>rhtr0hF?8)UZAz|~dKu=yiB z<~$T2;g{bJ{jrGh%}vOcVmYemIPtaX%vQy8#3VSXM$53*9{-rs z-n@Uu)FWxuGdAGnX)F-ajPWGkJ|(E64zw0H)Ldb!i^IHRJVi_Xwco(TFS^Z zYlxosA5oe5w;wCdsOiT$Oy{B8I`&wW&$3$eeQ?i5j!7(t>$E(|F>I&??`}8s?uazP z2(9npv}R~r*(u}mYl%cmH7r3>ytI=w4k#$Bzq`EFpv1UnoDHmKR!vO09?RhPbxfC_{N4T;mP~4> z68Bm~FPw-Z^+c_}z<*gvK5+_&QyIZb4E3$gglv;u;JI%?y4KF9A!&ZnGP(0Cz3E&9 zcH{2zZ44H-#{Zxn+nq-^|9L~Dr%R^p)XW*80=B3s>qY46OTGOgP57WQEKdRTJha)I z>3b~tyfQb`ZxliQTL3lRn&jy1zSr@D=n?n6;dRxh&w4ke@`mi$xzxP$2~Jx9>tJec zCV0W=j?D8D$p7xCOHbOlbF%rAzdUjdLfSdBpVtqX}c$>Pq zocM_0lY#|P-79T4h+iETSlg?Z%yq3ckQ7+=P@eT9mT;02iaUajP8H2Koc}=FSJv91 zb*C1pQ-a^bLdcZm6V|7ZsQh>j#p;Cg=Ljsi?zjSFuj|#b`ndeyTYRw}yMSxws}xbH zU~l-=Gz&2ZAAx6as!En~1!CE8`|4&f=H?%-_bP#TqEb&@1JpdM6F>W^36?z`&)ejA zK-Tk%Znlw7GE^B0Ndi&fHA!#kwLkS#a|ycHU1~qpw^S}^sYuKlxxq-Nf?+;dugq`x zYRXI7}65K>+tV*et;{Deumylcr?PxFsLJ65q-aLe2Zq1#D zZ;y>z?MLEax{l3Ko~-`fa^I<^Vm{NR^HZZMA>k%m!{5h$0~#gKO74!2&pJ&DRWRvs zKrYH}bURiNK|d~3&pA7;>*nl9suHYiaZ(IauTT!Q01|g0+Ij{UG|6S34hwkx zS%SAWp!mLZ_gN!SiDDq%N+c1XUX}{h1)j5$=`VN1H>oM@>nI)9K-naXOoBZ%$u7(( z9kj9c3wfiMi((^zs+RpfnON(vvSjkT(WTX^I>I%KI${4%nj8`}-2Y_v6oSOYG=W!f zWuknT1dzD)5B(iwlPv8tH$K!ejHYP$ z-cp;k;=!KXi`vZYILj^4S@=u7_AE0a#qt``x48Rfu(q_MR#kmD(%ro07weBs_#ZKH zE7AaP4$imf^=|*tI+4SZ=0gjc`M5@{CsRI&t&I9mELwe8J{iRroUi}b~|qPZd_ zw4J<7qrhHV*dlYuO6Yah<>@?F8Mu)VsesOa4(#NyN54#?WR_aXc}TG_cUh4vj%q zQ*MPF3ShD5z`8zG_&e)Jz#Asf< zFp`!1aU8TWw0Zcfc}49&yaE-3Bgrp1mL(6DnN0NV-cB6mup$wY4Njp`;c({kNNr`P zV;NGJ&i>1r>Q~4Ge|+VBI*TIp`_lRfF&E>n8mOJ#+h@;IQWgRUQ-Wj1@TiTdZSg%V zb)d#V5*2J2F>!-S1;RfMG+N5#%z1ZSV};^j8?lB>-a9@qjng#p^zRo2$$(D5#8#oI zd5NKM^fE}`+$&n~A$FosR4SaeE>5BOy2QH*Qt}o!5~RXy+upa|FCVU=7$`#Ri(|Y1 zLNuGN>)$Tvko6t3CfPk~|($&MQp?gE;ZbWFbarKBZ= zTY0f9Fx8kocJV4lyicz=X}D9i5h-o$TF!(;9BUs(MC)&w^YKZFq?Z<5ix|DaOxVKs zi}<#}#oy!y+flOmYpZ!-;-H z&$rc|Q4zl<0TD9g@tc%OjuIe`AxzIxGG*^ds>){;T@prN-Wwcv@*E4dgCA?F>qe`Q z(Jkw4y+vjO?L&V*h8$@u9U@h0A_lXF)t=5fg)VUQ)MP&#-!GSQ4l+8SGb)4Pz6o-{ zzdF)QYoWib=d~5EA4b;=@_idN7V>60nPwuLSE19{34Ntr3q9S<8B6|lZ&o#;oe?ND zAz)y$&(nM%u}=g(lhf~R+yK*{DsED@J%2{@%#7fn6VEonzRi}O@{KuJc4LMtXCGY< zk*z+IqB|U*L_3F>3N%HRN|;J`)dV`3`_M(lnqA=D$sG*PLuQlyK6N5t0FFuGq1Oo@ zQ{ZK#()pdZf$6`dk?Uf}iCM%PErRlTFGw^1YLpcNvUma57G6CIYsGKMp1c?9FW2aQ zrYQ}AG_#9X`Mc1Q(LPM2n1V?<7W^broB^rD(=Fn2tyc`LjKS4hYF8_cuhiNe4le;L zFyd7>1l@I$!y4M;%>~~MzX+D(DxyFQWyd=_RVdVRc2?^G7Lt6PGqkcE#k3S7Ep9L7 zzYw765PnG_+q)0`pqY+wB;m<;dh|`)&U^;b)#~lTtG|LrxW%cRj6#v>j8#y2mbB3i zA}ZpUshzq}IJULa($)EyB0en)^L>X0rd%8r30yJA4o)8qwefU-28FT*cl}XwySaAJ zYbMoy>a$g4BcC2ws47pxcyc&Te63Hp3@y0J$DcuwL$Gv5bPGU7@ALwZs{~qc^1bHa z(~N4ng_Lk4GCcZsY!o$eL|z1lUhbzWMn;(Dtnx@vU!seQm;*Ymuoo?IT1Qb zuX?*|cN+^Xe+b@QDRw?JezFhpE*PnKSDG^oOWhrIb@ z+}2Q(CEPhwOieFwtGpnxV$b+3=m;VV&NZH}&*YLXZ-m)UcF%EM#0Nh`$mO&J@-2de z%`xoy)IE$!3bVVATC`*-ID%sFS|oQ%r<`4@_R$-%FJzX&Sj;b~$pbGn`l!(23i>A? z1tw~Yl-lZ+cJf<0j_jNV=*w7~3i4f>3x~2329zo4Q4``?_fd#Wn17MrpR+|GT=#9f zJM12-x9P&m0|@rW|G>NZ=8Nbh7!Yr)?L|eOh#S^6;3}4*-}3OF3#04a!Cb>lVUCJ+ znT?5uyZ6A?6e9jCpO3v7shZyu#a1}X*Dy<#hMZrMCTBW_jTxxDQubg+hw>7Yb#-gY zS=rGQYINLLjUvcFLg1*;7{HD=8Z-%U4 z2xoDC!j|knU3@{{b~~G0&aIf5-02^8!*adcz3$LkWs>CNm+r7Z6!OePu2-?Ac;;W( ze1E)9NY9>Z&+c~RJBJILS_NL>q5Cl5MU7_Mpo6z)3&87+AtZ9H{mHhSIldmH!9KzN zvP^o?y|&asVn$v1fF_Ua$f7Ktd<2Ihv(v&b$wmiAcs8Kx|CqYU9_b3aOo0)1mpU8Q zs?zm*gV#}ZJ4<>p<>Ob`xhS92;Bw(Wm+}*P7jn{q--H)05#kWrrD$MyCMRbsIfhs> zg%Roa%ZkMk2Pqsq6^ZXAsXk>T-d^|4*JL| zxfQ7DuP=_*8M+LSidzX%1s(L-jji#(t-qgc@6st(P#8)k!8_hRo$y-0YI{W#mQwO# zXx2SX>XIttKo_gTU`f!0QGdX*@HP?Z-!~SbB|kOC`f8d9Js(=EZL>gwCNhejRESE3 zAcgGLO;w687~LOgOy^yDR*?H%c3&E)nfTD)V}o}{yuR!gtu|(qRiBFq686UP%XG!p zyQVTlDmx2GCYX;%H+=Jar#*}b8XY15YE4M(f2mxPBes)xEzIQ&(sO@Zk4jIquZFrB zyWkAmqW=m?$3LWW&dJ@4C|lnd#wM}lErV@vXB5~nba`OKPP{hJxhGEDz?gQ1q2^k4 zmpoPV?mZ6Sq_Q_?zo>;H2K+9KI6KC+>2UCQEKKuXexx`(hvU|VHYPz<+g_KMeKg5F zZ|F22bHK*wHL1(|_@o4iD4j1DIVna1RV0qV=Xf^;xdKUx>X2LXW)7oNHDPhfq-tCP z6zt|RCl)z*XMXEc-l$hmL%Q@#VxNfa8euU|2zp56U(hQ)I8@Pd+)bl69mT zcC3wSudN(B|MFPTd!|h%j$EQU{OO;Trap{{GQbUup$Rkf;+>YvT)uIlt1YS^^*jXJ zX&?5ncm%$bT}Jb7&CJI89B89O3UCY&hB-Jb`^0Xq)44Lk3sbXJS>2V`kv2g)~Q7hlAmHJ9v-y z`jmdX9o_3PnA*I@^_0YeW0*sW04$z>KQtgd)-SjnH? zKXH#R%yf1S?lnO8T6$};`blhD1scof=n(4v>1)mBThS2UA&1sEu>}b|h&=ai4 zOqhQ>`)#1sqR%9xQ%*n9$zlq1h|8D8FUSH{R6Qo3phfY0|9DpvLp+$6&VAi^g!chE zBGA2am!#YeVs-e#HEo*WVIR*tL0f-&F*IokdU}m(Ba|y1vEAn0oX`k`c62|607%A) zjmh>PM23g(Hq|(^eOiJ?2zr}4yeNJR9+~oH=FX_x?p`@+A9D5hkff2!B`TY!5i;R@ zWy(0zL*UHGkk|Ix6y1%>Yt@CA_VDa~eAj&+Cb%o7Y%LM?QucA{gu4-CEVT9JQQmaR z%!5XC(x$66Vw&|jsuHTS9~egO|3pur1e~PM!T&Zmuao{$9)4`4xNB2mLi0Gmn_&0FFcflgShb!; zQgOYL%qh9uQJ5$HH7uHaD@Fv7jeN8>ETA&Ecwbs^LLZe9lNvlW_W_;_Qpxfu!uW{} z1>tDl?n;=b46#stEpQ?|(+d#4>Zn3`y|>a=ebHU00%Q$+rR;X3AcXzRLzn^ei1hRr z?4(yCm)i-ZDS|-MH37+6LEjvMPBvtLvaxffmTWwc!F5CH>_r#{;uqen}c{uj`w&rYE`Hdl!J|7R7x=2 z6n^lA{QY_xTR2csb1NNb&foUPNFBnhJcHDE%)CW!;6PX$!xW3kypJ~Uu0)~Ny5p(w zX;%%$(AOo(xxD@t#Y)}=a8310;LJBK^@7xp7|lR^;{|m3H2F6APbHXVd7kx{Tk0L6 z!;xNns4r>}ej`0?tKqU`g}!5!_ibDsR51gU@?#IStLEV)J%e+EG*eCiMDH8aW}}hPIk9ibb|r4j({x0V`M@=7yn`)?5g>iu=lnQnf)=it?yA zskOBWVw-a;U&GP_L>G1VY;w#nu1%)0KBAlgMwVp}fBIaE^*c8P{Xx0l<)o~vI)LR+k-r~iT7quw< zh>Ne_Eg`#~sf&B<9g|HR_lDe`c$`zSwpD>1INJ|tVfRUb6AWCDh;Z48!vVJ1m))jy z)isP#6e%I@sw>*8=cCNMS=6GzwpKw&S_UQ8`SCIW`}PrFXa~% zvD*Mje0%cDES87SBGIb$-ria6)PoPgLQ}TcUJuxeq>eMF=`LlZ7!S6>VMw%UG0O>| zJyVd%m6}OA37dqPm_H-iRRV)c%X^5PvwaH;J#duHP>7awOI?QRFfL@^jZ0)V1RB@B0?4xG5A6 z%BA3*JsqWbS;?K6MN91B#R|hgd&(!jf!UQ%nC#gJ+knXg8(7tWrIep)*Fzg7E*ys+ zu+*4c5{dTJlaz=ZrbboP1F`NE)F^jEjM-F*Q9a!4Kj4taN_J3S`=52%)?Po5jGYQJ z{|BPV_J1U*oUH!?PMHZgI9ZtgC;R^rRZdQp|9hg^46c%_`-feoEZli$9#1&U*)8lC z2ow&1g%J)O1cjIgg_y2_RS6|9adBsdj7mbv`~0bU4(GRT^{qzpDz~W)&s_gZ=c}Ii z66w}n3Zg%|3=BEYBe%%Sg9|gsT*KZN{vDN@=7#|GuUr_w4!P*zz&0ht7qHTN- zvCkiMXaoy$(nZ0Z4Jq3HwK&ZXyYDf8ce{=z9Ro}-`nFFjbmw0i4cWDqBNfb8JFQp_GEgu@$H70oxEBjUj~juQw8Ffj-S zh!KhqP(2UOwej8bZ&!Ch9nO0k>N`%aInwzZgc~U5ZW0ir5bnU6pZgC!Ap;{=|~ z=Wp3jA000t(mqgwILLLs91`YkU)A1_!C2q**Oa)RHxLHM+a@RonD6h8rsmGn6fi>2 z=MN8H?)z~{U_nJ)`Rpg^L4Y3|ydAMWPhA73pN5hc2zHjP0fY7h)fuQ4( zQJhoou+H`_?m{2W>zfWJwl6FQ^?t9#dH<~v9F+5i&QTf|8Tji9@%~ry(ogB<7wxBO z@>llwcPl=U0_}5b=3(sj*C9xUNMWxJ^j7pLqMHE7=KUM9|A%844X`$E8H7ieTl;&Z zDjs+X`4|5b?E4Ip2%j2>pgss6%;FA^ru8!z<0p@W1_F9Dz(?4ZhYoc2y#k24^KHJ) z+ZDjWe@g@$f$Yi8`q@>$HHGm2@R|N1D*{0U0DTR$mlcaaF!1aKAX7H zwPY^26EiGZfE$iwy*?}XrQZ*_y$z}zW8(vsoo6~=OW~*1+l2y;o~|xo+pIsv%U^O_ z`59ul4!e5eHun(m#Zi*Jn@7c`k|*lylZ2e(nS(}z?V&D8+`~A=m{yoSy6JS?R8E1} zkjUf0zCAq78){5`ZZv!keuwGbu+tIv?FbC|yMQK!w+q)nn}Q|j`GU}h&`WS4!gq4J zU+|2+A&+K|(PUq}!OvE+e2_En5D!Rh+f#Skdn@=74I#urednuG-A@KX|I0OpKcj1= z9qCm>il|F5I~2KYW8@tB0_nI^L77444MQvptgJbCO)R~gg*lm6)g90g*y(K7z)Q_f zpXK%+PtU%GT=8z3?(>Q(T`PFjZ^A7q>8oS-VuyU z7f%x37-*QZSHBs{Y1Jk{pJqBN1f(k%HPKQ(=LR&W zs;X8ynUpsXP5w8Rj^yzp9!4sbAAlCAe4c|3L#CTS7kjZb5o@>b;k2RGOLeixK&CaM zt)qv^DPG0=ljVp6E$!LKpP+p=I{eOx%EyI&cXMmxn+`YWZ!u`yn7UVoP_i-j`Ze&) z-F>g8RBGx*rVQx|x69iJzQ~NmY&9zLaxY98v49f`-FgGnrdx2x$)IR)*g6ds_Otm6 zn@q1u8Q*Osnt4oY-DBo2x}s+J7=&u3*O=;tci|~o0Vua+&|(oIrGu6=G0SgN0 zI4+|?TfCynKQTQgR%RA7OJjWjX|J7MOlav1Ss`E&rVww-Kp&#lSW#Nw+r@545t{T> zz8Q|{a1JkVQ+%{l7?ScOL(=%#t?5OLv{Vyf*nVSpyWJQ*PqxeAY~lo~szON^qAds& z201d5M%mZ{ODG}*<;~+#B%d8>NW&ADN0_#+xMRLql-Q7_vYvrC&0W;=A7Q`|x$%w& z#+Y>`WXL=Vk2m!IVfaB9{^^WZYSEa#Xz(UXFxp*xn5$L`QoN@~Ne8b7sXGypEzp_6 zN&kKdcf+Wa<#uJLi6tF&1>i_DL8xzq_CFVcw1ey(9>lHld=h7iAz{$K_ltKW{dOJr zsw=v(XEm-J__d}Hw5hkCM=NT+-`w$8(p|+De)68ffgQF&j=@o_2R$*ho@;;Rm=XLv-$+adRnuIL{7bNPs@+ZhdZ_O_%)H(z^VXdNwi<#7sF{NZHqTOgY(mYj-m z1;Ree@sh_*LRvX;dM=hJQgo8-^^l#soN<44?sdXNEMnat z*#vh1AC=injjFtAs2B9R(Mef-B3Gi-ZdSOB4TAJ6Waun+C};gDTL;t3NxY^8=w(|y zE0;XF59V2oAqJ-Ig$FBe#y;mipe)QmOH#MI7qY>&ox8o;G;0zoBxPB zNm$}B!OF5;*sLmu&FeGJ5bN5ViO7)JqF<@&VCT&~M;skJ2kUUP{6MpX7c*V21Mtu;xH-+ZI9-jUh# z+SBDZzLcRLo}_%5(mA`)05?-&?5MR~a&6#oL`g&Wz?0u%DVVADoDAejd?tU)4u#PI zWG#*yLlTpYL~1^INS|dWR5`?*inj+LBXbBYI$o8E|(H1BaEiAD~7YE z=EH9@A9%+w*{$*lYedF>hG1GjEyT_}mixgIL{7m@&DSM`|Mw&enBvs@a# z-j6LY*(4$5NG+R*_~TZ?ag*-;)2ByWz>9YBQvT06BUic&!{`p1+q$l{1IS80up{5? zM5doY$6Ms&N=sa_pb5r^(BV@qAI?pwM7*+xhh$051ztDE2Xc4#+WdN{#!8yKiz*$A zlMP=fD8D15$LPtRmnyrNTvi-f7+w7ueY(5}ybIR+)QLO-uJV}5^I8I+W@qDyjb*|JfW?Ii!Z9Bj@;ZcVxv@sz*?0DK46VIrSsxbSWGk8@b zA_aeGN9wXN#Daq}XJ1H5Nndk^JtevYP1|&7iYV5Fr!)1WE=kd^UA&@mT*+3L#tpeb z`N!)^S#+VyQPEz>=>tCx>>8tCGw~BuJQ#xgww6-ryQa1b7JYtWi{1L0bEHGoEdzdg zYU~`MeaUQ1cFYY#obkw4r57>H%%?&NwP3zh zYGEx?d^!dNU$RU|taiV29Ys5tmNk7G8bqq!b1W?ibC52M|=mL%7D7M*?i#3!_o$pW*5TNJ2 zd*S2@EKAy)_!#?=J3L~fre+rTQeHp0&w$|jXm*q6qY?xj(r*5bL4vdaR`H-{MW#iJ?=Uro9oGUe#|u-9v$jH+EN%`OM7B#_IxD);AvTI zkfGHwb|`0tPsL|nj8NKl=>925d1n3Si++8&)0YR&#K>8HqAm-CDJUQVnAzyKb?RtW|-9dsUxN#jjHk<1eqo>N2_OW58d_nwVlEqK+$_-Ny-(9r&j8~O^#gkivl z6B)qE(>lYVKD>G`No+09f7v-CDVKH(8s*d`<~P+_#lU?UlQP6nY7nTme+b|lS&%@KY>4#yIfDI~! z`IR`cckLtIVS+2JI)=ruM~UktUNX^Xqo1#%*eCu=^W88g)7ObETTg^>kK6Cfyee@F zsNWM35Sr>(&vrZdU=bd!VUPgJuQ9LHVr8NgWe7l)whB>X6*7z!!pEbhK*_GJXC3?- z(%4~j`AX^dU$1du(JfsT8WPih0W*?QQlfOyNo$HNY0{`* z7F8jGx2Vo;Df2jv$##*}Ym_&SWcv8bRd};4i9!7x4>Tk-amnp#*R6)B0)q@S#ioJB z(kt2^jwL+j*MVzM&J&nW@r;D|%J6Yv=;YeZ;`&gG$TtOLS%5 zK><)H)}uZeF$L!j+9PL`@@c32u9WfkZl zseBT2T}14fZ?C+JZ4-OMNed>m19{4|RbiOk(KnS{qX2|96IHw2nxKo9>4Vy=GtsW- zl;gx*y0+SNmX{n=qLbkG?miFSY!gGkeA8X^g|@@qbW7+nb8~q4H>17mju-Zj)8pVc zh9cKEzsHNGO`__KWi$)CDq@-@Gb*(wY?RluTt9vzI}1s&<>;EB^8n8Y_k`VGCmxR* zJ&B?1c1Yuxxg>XM3a`5|F@Z*a8z9s)xU`b1(Kw2A=Ox>gKaUFcRimj)|3)?Z*$8ok zS+nYg;whtP+uB9Dbu3kxVE=cPhaAmS4pK8qDJjbj?~oJC^Qn2)-;U$^c{GZzeJUj` z-KXEaM)tz#7jF42GeC(pf%h%o<3HDvi)PuCT+K@vjH)~`&WiJO)F#&cmwvFsPr3tO z>ty|Bg{0f`AT6bzS)+J{fh!WL-u9p4)f{~>P`4Vh)De7O!`y=X>M`9HRR>>=rm!dN72Y>xCoECWQk>>eO(jM(>e&` z8C7CsZWZQi+H(^GG}KoQa)`IaeOc2?YWt=Ok27rlgQf9?_Q z!xWZ#lE`;Y7RgkR3G-##^;x>lQB5z4!-eJ)KRoyJZ|olVu?8%f*k9c9#V>~{@mqDh zWibQuc*KL#f(r_n>t*q@I=& z)%JQC(s-M^F9EgeP7XBxMZJ#CN~KX;sbouXy4L&8Wt4Q-LT!8Id}q$=ZLsMKSk0y$ z?4QaK_~TM}yfV!;gf6Rq163@l(JzWQ{OmuZq;OFa*ABi@0+OmhJ+neqw6sZoj5iK3S6Fk^$xBx zZ_f^wFqu=n)|;+o_kx7E;ylfp#`?$FIE(pe9|5~fm>sW$&T$Sm4adnRxj3?Gi1bv# zRm4n3=rPYJrdsv%pyC7U>&dcWnTLH_-FAJkiiHjg3M<(rhI&MA|Eg7bX7yRm=<6Tr zEyXT4g*H%$pTJc~@EtA~(wI;Lpowa#U7oj95>&+?0&va#C9oxKr)8;e6|XOL42`j~ zTInK{C)1w*uDh+dBhVLVuh;VnRnBlZ#yE6sf=4ZE!np>e2@swTx(^28ybG1*4TYrNtanIBi<~qJN&$?dWns2#0ws$$#=@w*wJ=4X$UiSXbW1e zMAIvA3m%S16kWWfLznAoK3FoWCh$?S^#AcOqu!CVFN1?jj9JoU0Lmup5kjKPzk9#W zA9U0w>_zVKCJ+Tyw5hL8RDAKM9X&)WOje(Gk`~ss~+C{9b z9@sv@q6tvB{w=~Z|FVc$YK*o~6^wiV0EkV~yCvxT@%kJIA;7~xFKksLhDcH+z@*;z zA=qjujQu}rVfzG$u=hahn94&E#tMSVQp6fIR_fEr@v~|3*zv1ZQ}V!CS}?GN&o~2p ze}dh`qjvZfW#eON!lQPjFMJ(4zHBIv%Jxy_eE|n~RGq&0eu+-mRoIHgG=mgQTc+fq z5pP~jQp*{?v2N|~&e{iWodG2=vIFv_Rt&aw_Q*2-MuOr^vrY3-bG@yNy2)ll5ZjpI z$OuUI!zgvn`YCBtq@)gP8~KW%NODWo7rMkBk$OeKU8xD4a+<~UNAXaw!-q~F1<`NX zul%v#Zw^JQ%)wFk6=m2`@K7Aj1<;enk;>}=ykop4b+nbCqVLJDz@;HePoo+% z^yjbBt5UvhRcfDwWwGmxuMQ^9|GsuwZYm9sWW^2~LFTc7TUZx0!bSUReQf)`qwRe0 zz4IP<%vJHtxFVyOQqG#1r#d0+))OAJu$i>-3i>atK~q z)W1SIrR^<6)Pzv=i_f-FPHWv&glxIuPzW{L^pW=N0dK7tEhZkIueMAJ>B5tS+wde8 zw}>r*qPP##2jBlDY^G3)2sqWgEDa@mH%nwH?iQY4+aeG>Zm4I)`nTVzC<5thO$Gjx zwFKz%KWB?}_r1g<&#g{#GM2Gx4;2ZKH20(fkrd9FWidQ@wbEj4ZBE9q?GoyHjm5%Rq2O-Sh&uaa~>f% zn)dQA?y!!342|o@(&YzVx+F1u-sM$5(QfpE*K`%AabwmIYW(NP?D=9KG58QFh_q!X zTl>-QM847jo;I^+`IAPG!W$+;grcL2DeF_EmeVlW*;2YCn!_ZJFjL+iJ7G1-wpxBn zRpCAj;6k2%%{JlG%=Q}ePmFAmX`cYITnM$FB&afPAAe~tQ&FKL_(6ZbfI z>pq|0qgY2)b^Z=z1(}5H>h%7S)40`X6>bMP4U6avH~C^sY@Pz->5aXaGF{=Pe-9VQ zXrekh6o}TR2kLmD>MX0tgG@0~`W(9Yz1M|JexS!{V6Cij3Ke%9u{&$9P83wCGLVX8&^6Aa#E~in^V=c$N%5~DT!8f-3aS_ zlE$%1n35CJL0>Mc*%wM=dqz0Ap`7$>4i1iPAIK@Tkqcxkz7mnpCiXy6HTg?EZjuG; zj%yi+u{*KLP^d;U10;y1ACe>MFfUdwD4I&dw=qpGyoV#Y1v7h9{uw_>it?%_-7jC* zKlHbAr-_VF1Wb|%Fph0IxPJZ1;9D+QXtSz9B^b|XW3s4Ims-DV#lRxOq(-~{&jxlh zTX>Z5W&a}^W@~FjK57^ku`A#D{tTTkEdkMYRUk@R8)+1V76=F8MOR<`y&Ft=R3+C7 zbsT7MNc8G()3srVHp+U^eMTkKL*^o?&NJUAy_F6EO?&$3mSN*&>bMjT(av&etGuT_ zxeoyFvr(E~ReOlYH&wqNSNp4-qrjl#16t!-NgU)~b>&%>)b7sze=AGZX z@B4e+-}{|sp68u;XP)2Z$J%2*v>}d_P!8XS-<}Kb2v1*EJr|}KuNkOe(PrX3X8VQD zSL8k2n<5-8v^){!NzStnDY-d_HM)<*4RcW>*efR~QV@8qJ^o3{<>Wn(T0oms8L7Yd{Xv5V)zjisHq`n6%kXIeA;- zP)@`hSGT$ejTWQ`iqwRl;9G9-Aic?BfNi|at7wF6c&`TCupZ*^GXe``e)&aY+sLEUrzr-OLm+Pl!o^_ zcg|@`dvsQ)%idPAoPvhkIgOn!{3<+pB&qp+Liw}#5^Epf9WTZH(2Cb1US5mBo48(z zRQ<}K7s`|8WJPx~QV-cj&bEb&Glga69Ygo;Gm{w{)z2JdMC+6anwIH+W)mL=&`o#jZ z_w7S=ha)WmPuM57t{)V?lcJGdbRrirE*Fzj&hX%0k5ydnwI=ESv5swYKnb76kDeh+n4U&(|#oVg%9lt($9Jlz>qA4X6x$ftac#c)>v4QT zmjzdYclFov$p>ut2Q+$1tnjs_`e^-r(&ZiFf4c4g4-U zepTg&;f2|4jm10T1*0kHX=?hs3K#F^*@&5VNd>MUee{NF|4Z3^b-+o}g^Q4*KC*N_ z2ti`oU=x#$4^2Zp8(-{6oWC-mTmk^=uzp^z%c z$$|H3iDUG~d2s&^SE~G4B@*7HGLV&lCH9CR(<Fcb5TI6P^J?lj8yT;W(9;=dWj zC4bGyB-c})S$)`4SuCDCNF5g`tFn6O0`5)IY#14-X@6XA?&YB%`Zmx6<`#X*=!L+h z?Cr++m%0I!a7~s$^Dyes2F93!A;w^^vD}WpqW_x-DV)Y; zGw5>63@wDiPz4<(;XQ$Nks%>|G$wOZ3n?&&1CY0Gnk)eBjBt*8YXA%gk#i0(P$a?< z3Pk>?^?wQhPC+La0J#_p2*>aXqA^VY$Jw-qKn{ZjIPrZs5-9(G=_=6XJ6Hkp7f+C) z*$e>4#V?o`5vmGumSb^NaX8_e2mo5%bNa^0L7=|Z{s8`+m2-m>%IXDce*HuZGei+a zbI?yy6V0ZfUJ?lTaA>!t;d6GP{Uux#ZEjGOQ)<~segVgaO~%B0y8Ya;W7F*`JU#auSk$8dkh5m(1+O9s`JP} zb~(o8dOR_Sg;|s?EFP^0K#Cvaybt;w#9nCUp9VLb%Fl zp`^wUKdLbYey;FYS_9-sn_j`POQN$XM*(H!#qBR+d6_oK?;>>ai2Tqyrqu(;K}|JkD|;t5==OGRC4|}3mnV0AHFJ6O;hu<5*?%{b@7!*( zA~`%e*cd$G5Z337#KO&j{e6P1D?>i-=I;A>%{?8*dL%RdkL@d^Z;uTPW1@cHSBm2j z=Be2FiQj%*qK)139wJo1!7Q^Hv{2n5&;YikEV!*Te1fPXiU@A5rKkjQVu5y1bEB-(8dbsL*) zIQfC?chP=}Rc8H#yI)SIw=B0@L9LBVPA?S=(9dl=S(`t`yX#qNd%MLjQopOiy??I| iv_Ici>A~N<#EGDVM?{6o{Q^OwF%Z?=yYVh|s{aM?)hZnT literal 0 HcmV?d00001 diff --git a/vektor_addition.tex b/vektor_addition.tex new file mode 100644 index 0000000..9e682fe --- /dev/null +++ b/vektor_addition.tex @@ -0,0 +1,39 @@ +\documentclass[10pt]{article} +\usepackage{pgf,tikz,pgfplots} +\pgfplotsset{compat=1.15} +\usepackage{mathrsfs} +\usetikzlibrary{arrows} +\pagestyle{empty} +\begin{document} + +\begin{tikzpicture}[x=1cm,y=1cm] +\begin{axis}[ +x=1cm,y=1cm, +axis lines=middle, +ymajorgrids=true, +xmajorgrids=true, +xmin=-0.5, +xmax=7.5, +ymin=-1, +ymax=2.5, +xtick={0,...,7}, +ytick={0,...,3},] +\clip(-0.5327923283402358,-3.438438462661708) rectangle (7.550357053950259,3.4379509853468746); +\draw [-latex,line width=1pt] (0,0) -- (5,0); +\draw [-latex,line width=1pt] (0,0) -- (2,2); +\draw [-latex,line width=1pt,color=red, dashed] (2,2) -- (7,2); +\draw [-latex,line width=1pt,color=red, dashed] (5,0) -- (7,2); +\draw [-latex,line width=1pt,color=blue] (0,0) -- (7,2); +\begin{scriptsize} + +\draw[color=black] (2.55908371629915,-0.25) node {$\vec{y}$}; + +\draw[color=black] (0.8,1.1993756042973518) node {$\vec{x}$}; + +\draw[color=red] (4.315669182768639,2.3) node {$\vec{y}$}; +\draw[color=red] (6.45,1.142250873680458) node {$\vec{x}$}; +\draw[color=blue] (3.1,1.220797378278687) node {$\vec{x+y}$}; +\end{scriptsize} +\end{axis} +\end{tikzpicture} +\end{document} \ No newline at end of file