The angle between two vectors $\vec{a}$ and $\vec{b}$ with magnitudes $\sqrt{3}$ and 4 respectively and $\vec{a}.\vec{b}=2\sqrt{3}$ is :

$\frac{\pi}{3}$

The correct answer is Option (4) → $\frac{\pi}{3}$

$|\vec{a}|=\sqrt{3}$

$|\vec{b}|=4$

$\vec{a}.\vec{b}=2\sqrt{3}$

$|\vec{a}||\vec{b}|\cos θ=\frac{2\sqrt{3}}{4\sqrt{3}}⇒\cos θ=\frac{1}{2}$

$⇒θ=\frac{\pi}{3}$