Find the angle between two vectors $\vec a$ and $\vec b$ with magnitudes $\sqrt 3$ and $2$ respectively, having $\vec a \cdot \vec b = \sqrt 6$.

If $\theta$ be the angle between $\vec a$ and $\vec b$, then
$\cos \theta = \cfrac{{\vec a.\vec b}}{{|\vec a||\vec b|}} = \cfrac{{\sqrt 6 }}{{\sqrt 3 (2)}} = \cfrac{{(\sqrt 3 ).(\sqrt 2 )}}{{(\sqrt 3 )(2)}} = \cfrac{1}{{\sqrt 2 }} = \cos \cfrac{\pi }{4}$.
Hence, $\theta = \cfrac{\pi }{4}$.