Q. If $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ are vectors such that the $\left| \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right| = |\overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}|$, then the angle between $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ is
A) $120{^\circ}$
B) $60{^\circ}$
C) $90{^\circ}$
D) $30{^\circ}$
Explanation
(c)
Given $|\overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}}|^{2} = |\overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}|^{2}$
$\Longrightarrow 4\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = 0 \Longrightarrow \ \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = 0$
So, angle between them is $90{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.