Q. If $\left| \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right| = \left| \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} \right|,$ then the angle between $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ is
A) $\Pi$
B) $\frac{2\pi}{3}$
C) $\frac{\pi}{4}$
D) $\frac{\pi}{2}$
Explanation
(c)
Given, $\left| \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right| = \left| \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} \right|$
$\Longrightarrow \left| \overrightarrow{\mathbf{a}} \right| \bullet \left| \overrightarrow{\mathbf{b}} \right|\sin{\theta =}\left| \overrightarrow{\mathbf{a}} \right|\left| \overrightarrow{\mathbf{b}} \right|\cos\theta$
$\Longrightarrow \sin{\theta = \cos{\theta\ \Longrightarrow \theta = \frac{\pi}{4}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.