The angle between two vectors $\overrightarrow {\rm{a}}$ and $\overrightarrow {\rm{b}}$ with magnitudes $\sqrt 3$ and 4 respectively and $\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} = 2\sqrt 3$ is

Here, $|\overrightarrow {\rm{a}} | = \sqrt 3 ,|\overrightarrow {\rm{b}} | = 4$ and $\overrightarrow {\rm{a}} \cdot \overrightarrow {\rm{b}} = 2\sqrt 3 \quad$ [given]

As we know,
$\Rightarrow$ $2\sqrt 3 = \sqrt 3 \cdot 4 \cdot \cos \theta$

$\Rightarrow$ $\cos \theta = \frac{{2\sqrt 3 }}{{4\sqrt 3 }} = \frac{1}{2}$

$\therefore \theta = \frac{\pi }{3}$