$a=(3,4)$$b=(10,5)$$c=a-\frac{1}{2}b$$c$$|a|$$|b|$$|c|$$(a,c)$$(a,b)$$c=a-\frac{1}{2}b=(3,4)-\frac{1}{2}(10,5)=(3,4)-(10\frac{1}{2},5\frac{1}{2})=(3,4)-(5,\frac{5}{2})=(3-5,4-\frac{5}{2})=(-2,\frac{3}{2})$$|a|=|(3,4)|=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$$|b|=|(10,6)|=\sqrt{10^2+5^2}=\sqrt{100+25}=\sqrt{125}=\sqrt{525}=5\sqrt{5}11.18033988$$|c|=|(-2,\frac{3}{2})|=\sqrt{(-2)^2+(\frac{3}{2})^2}=\sqrt{4+\frac{9}{4}}=\sqrt{\frac{16+9}{4}}=\sqrt{\frac{25}{4}}=\frac{5}{2}$$=(a,c)0$$()=\frac{a,c}{|a||c|}%TCIMACRO{{=}}%%BeginExpansion{=}%EndExpansion_vgl.b.\frac{(3,4),(-2,\frac{3}{2})}{5\frac{5}{2}}=\frac{3(-2)+4\frac{3}{2}}{\frac{25}{2}}=\frac{-6+6}{\frac{25}{2}}=0=\frac{}{2}(90^)$$=(a,b)$$0$$()=\frac{a,b}{|a||b|}%TCIMACRO{{=}}%%BeginExpansion{=}%EndExpansion_vgl.b.\frac{(3,4),(10,5)}{55\sqrt{5}}=\frac{310+45}{25\sqrt{5}}=\frac{50}{25\sqrt{5}}=\frac{2}{\sqrt{5}}$$=^-1(\frac{2}{\sqrt{5}})=%TCIMACRO{{arccos}}%%BeginExpansion{arccos}%EndExpansion(\frac{2}{\sqrt{5}})0.463647609(26.565051177078^)$