a. cos($\vec{a}$, $\vec{b}$) = $\frac{\vec{a}.\vec{b}}{|\vec{a}|. |\vec{b}|}$ = $\frac{2. 6 + (-3). 4}{\sqrt{2^{2} + (-3)^{2}}. \sqrt{6^{2} + 4^{2}}}$ = 0 $\Rightarrow$ ($\vec{a}$, $\vec{b}$) = $90^{\circ}$
b. cos($\vec{a}$, $\vec{b}$) = $\frac{\vec{a}.\vec{b}}{|\vec{a}|. |\vec{b}|}$ = $\frac{3. 5 + (2. (-1)}{\sqrt{3^{2} + 2^{2}}. \sqrt{5^{2} + (-1)^{2}}}$ = $\frac{\sqrt{2}}{2}$ $\Rightarrow$ ($\vec{a}$, $\vec{b}$) = $45^{\circ}$
c. cos($\vec{a}$, $\vec{b}$) = $\frac{\vec{a}.\vec{b}}{|\vec{a}|. |\vec{b}|}$ = $\frac{(-2).3 + (-2\sqrt{3}).\sqrt{3}}{\sqrt{(-2)^{2} + (-2\sqrt{3})^{2}}. \sqrt{3^{2} + (\sqrt{3})^{2}}}$ = $\frac{-\sqrt{3}}{2}$ $\Rightarrow$ ($\vec{a}$, $\vec{b}$) = $150^{\circ}$