Q. If $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = - \left| \overrightarrow{\mathbf{a}} \right|\left| \overrightarrow{\mathbf{b}} \right|,$then the angle between $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$ is
A) $45{^\circ}$
B) $180{^\circ}$
C) $90{^\circ}$
D) $60{^\circ}$
Explanation
(b)
Given, $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = - \left| \overrightarrow{\mathbf{a}} \right|\left| \overrightarrow{\mathbf{b}} \right|$
$\Longrightarrow \left| \overrightarrow{\mathbf{a}} \right|\left| \overrightarrow{\mathbf{b}} \right|\cos{\theta = - \left| \overrightarrow{\mathbf{a}} \right||\overrightarrow{\mathbf{b}}|}$
$\Longrightarrow \cos{\theta = - 1}$
$\Longrightarrow \theta = 180{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.