If $\theta $ is the angle between any two vectors $\vec{a}$ and $\vec{b}$, then $|\vec{a}.\vec{b}|=|\vec{a}×\vec{b}|$ for $\theta $ equal to ________.

$\frac{\pi }{4}$

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

$|\vec{a}.\vec{b}|=|\vec{a}×\vec{b}|$

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

so $\cos θ=\sin θ⇒θ=\frac{\pi }{4}$