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

$\frac{\pi}{3}$

The correct answer is Option (2) → $\frac{\pi}{3}$ ##

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

We know that, $\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}||\mathbf{b}| \cos \theta$

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

$\Rightarrow \cos \theta = \frac{2\sqrt{3}}{4\sqrt{3}} = \frac{1}{2} = \cos \frac{\pi}{3} \quad \left[ ∵\cos \frac{\pi}{3} = \frac{1}{2} \right]$

$∴\theta = \frac{\pi}{3}$