If $\theta$ is the angle between any two vectors $\vec a$ and $\vec b$, then $|\vec a \cdot \vec b| = |\vec a \times \vec b|$ when $\theta$ is equal to

•
• $0$

• $\cfrac{\pi }{4}$

• $\cfrac{\pi }{2}$

• $\pi$

[Correct Option is b]

As we know, $\left| {\vec a \cdot \vec b} \right| = \left| {\vec a} \right|\left| {\vec b} \right|\left| {\cos \theta } \right|$

and $|\vec a \times \vec b| = |\vec a|\vec b||\sin \theta |$

We have, $|\vec a \cdot \vec b| = |\vec a \times \vec b|$

$\Rightarrow \left| {\vec a} \right|\left| {\vec b} \right|\left| {\cos \theta } \right| = \left| {\vec a} \right|\left| {\vec b} \right|\left| {\sin \theta } \right|$

$\Rightarrow |\cos \theta | = |\sin \theta | \Rightarrow |\tan \theta | = 1$

$\Rightarrow \tan \theta = 1 \Rightarrow \theta = \cfrac{\pi }{4}$