\psset{xunit=0.75cm, yunit=1cm}
\begin{pspicture}(-3.75,-1.5)(11.5,6.5)
%%%%%%%%%%%%%%%%%%%%Koordinaten
\pnode(3,4){A}\pnode(10,5){B}\pnode(5,2.5){C}
\pnode(-2,1.5){D}

\psaxes[Ox=0,Dx=1,Oy=0,Dy=1,linewidth=0.1pt]{->}(0,0)(-3.5,-1)(11,6)%Schnittpunkt, x0, y0   x1,y1
%\psgrid(0,0)(4,4)
\rput[c](11.3,0){$x$}
\rput[c](0,6.2){$y$}




%%%%%%%%%%%%%%%%%%%%%%%Vektor a%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psline[linecolor=blue, linewidth=0.5pt]{->}(0,0)(3,4)
\rput[c](1.3,2){\color{blue}$\vec{a}$}

\psline[linecolor=blue,linewidth=0.1pt,linestyle=dashed](3,0)(A)
\psline[linecolor=blue,linewidth=0.1pt,linestyle=dashed](0,4)(A)
\rput[c](3,-0.8){\color{blue}$a_1$}
\rput[c](-1,4){\color{blue}$a_2$}

%%%%%%%%%%%%%%%%%%%%%%%Vektor b%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psline[linecolor=red, linewidth=0.5pt]{->}(0,0)(B)
\rput[c](5.5,3.1){\color{red}$\vec{b}$}

\psline[linecolor=red,linewidth=0.1pt,linestyle=dashed](10,0)(B)
\psline[linecolor=red,linewidth=0.1pt,linestyle=dashed](0,5)(10,5)
\rput[c](10,-0.8){\color{red}$b_1$}
\rput[c](-1,5){\color{red}$b_2$}



%%%%%%%%%%%%%%%%%%%%%%%Vektor 1/2 b%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psline[linecolor=lila, linewidth=0.75pt]{->}(0,0)(C)
\rput[c](2.5,1.75){\color{lila}$\frac{1}{2}\vec{b}$}


\psline[linecolor=lila,linewidth=0.1pt,linestyle=dashed](5,0)(C)
\psline[linecolor=lila,linewidth=0.1pt,linestyle=dashed](0,2.5)(C)

\rput[c](5,-0.8){\color{lila}$\frac{1}{2}b_1$}
\rput[c](-1,2.5){\color{lila}$\frac{1}{2}b_2$}


%%%%%%%%%%%%%%%%%%%%%%%%%%%Subtraktion %%%%%%%%%%%%%%%%%%%%%%%%%%%
\psline[linecolor=lila, linewidth=0.5pt](C)(A)
\psline[linecolor=lila, linewidth=0.5pt]{->}(A)(D)

\psline[linecolor=orange, linewidth=0.75pt]{->}(0,0)(D)
\psline[linecolor=orange,linewidth=0.1pt,linestyle=dashed](-2,0)(D)
\psline[linecolor=orange,linewidth=0.1pt,linestyle=dashed](0,1.5)(D)

\rput[c](-1.5,0.5){\color{orange}$\vec{c}$}
\rput[c](0.4,1.5){\color{orange}$c_2$}
\rput[c](-2,-0.8){\color{orange}$\frac{1}{2}c_1$}

\end{pspicture}