$\lvert \vec{a} \rvert = \sqrt{3}$, $\lvert \vec{b} \rvert = 2$ and $\lvert \vec{a} \times \vec{b} \rvert = 3$. What is the acute angle between $\vec{a}$ and $\vec{b}$?

Explanation

1. 01

   $\lvert \vec{a} \times \vec{b} \rvert = \lvert \vec{a} \rvert \lvert \vec{b} \rvert \sin \theta$: $3 = 2\sqrt{3}\sin \theta$.

2. 02

   $\sin \theta = \frac{\sqrt{3}}{2}$, so $\theta = \frac{\pi}{3}$.