If $|\vec{a}| = 2, |\vec{b}| = 7$ and $\vec{a} \times \vec{b} = 3\hat{i} + 2\hat{j} + 6\hat{k}$, find the angle between $\vec{a}$ and $\vec{b}$.

$\frac{\pi}{6}$

The correct answer is Option (1) → $\frac{\pi}{6}$ ##

Let $\theta$ be the angle between $\vec{a}$ and $\vec{b}$, then

$\sin \theta = \frac{|\vec{a} \times \vec{b}|}{|\vec{a}||\vec{b}|} = \frac{\sqrt{3^2 + 2^2 + 6^2}}{2 \times 7}$

$= \frac{\sqrt{49}}{14} = \frac{7}{14} = \frac{1}{2} \Rightarrow \theta = \frac{\pi}{6}$