If $\theta \in [0, \pi ]$ is the angle between any two non zero vectors $\vec{a}$ and $\vec{b}$, such that $|\vec{a}.\vec{b}|=|\vec{a}×\vec{b}|$ then $\theta = $

$\frac{\pi}{4}$

The correct answer is Option (2) → $\frac{\pi}{4}$

$|\vec{a}.\vec{b}|=|\vec{a}×\vec{b}|$

$=|\vec{a}||\vec{b}|\cos θ=|\vec{a}||\vec{b}|\sin θ$

$\cos θ=\sin θ⇒θ=\frac{\pi}{4}$