If $\vec a$ and $\vec b$, are two non-zero vectors such that $|\vec a.\vec b| =|\vec a × \vec b|$, than the angle θ between $\vec a$ and $\vec b$ is

$\frac{\pi}{4}$

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

$| \mathbf{a} \cdot \mathbf{b} | = | \mathbf{a} \times \mathbf{b} |$

$| \mathbf{a} \cdot \mathbf{b} | = |a| |b| \cos \theta$

$| \mathbf{a} \times \mathbf{b} | = |a| |b| \sin \theta$

Equating:

$|a| |b| \cos \theta = |a| |b| \sin \theta$

Cancel out the non-zero terms:

$| \cos \theta | = | \sin \theta |$

This is true when:

$\theta = 45^\circ \text{ or } 135^\circ$

$\theta = \frac{\pi}{4} \text{ or } \frac{3\pi}{4}$