a) $cos(\overrightarrow{a}, \overrightarrow{b}) = \frac{\overrightarrow{a} . \overrightarrow{b}}{|\overrightarrow{a}| . |\overrightarrow{b}|} = \frac{1 . 5 + (-4) . 3}{\sqrt{1 + (-4)^{2}} . \sqrt{5^{2} + 3^{2}}} = \frac{-7\sqrt{2}}{34}$
$\Rightarrow (\overrightarrow{a}, \overrightarrow{b}) \approx 105^{o}56'$
b) $cos(\overrightarrow{a}, \overrightarrow{b}) = \frac{\overrightarrow{a} . \overrightarrow{b}}{|\overrightarrow{a}| . |\overrightarrow{b}|} = \frac{4 . 6 + 3 . 0}{\sqrt{4^{2} + 3^{2}} . \sqrt{6^{2} + 0^{2}}} = \frac{4}{5}$
$\Rightarrow (\overrightarrow{a}, \overrightarrow{b}) \approx 36^{o}52'$
c) $\overrightarrow{a} . \overrightarrow{b} = 2(-3) + 2\sqrt{3} . \sqrt{3} = 6 - 6 = 0$
$\Rightarrow \overrightarrow{a} \perp \overrightarrow{b}$
$\Rightarrow (\overrightarrow{a}, \overrightarrow{b}) = 90^{o}$