Q. If $\overrightarrow{\mathbf{a}}$ is non-zero vector of modulus $|\overrightarrow{\mathbf{a}}|$ and $m$ is a non-zero scalar, then $m\ \overrightarrow{\mathbf{a}}$ is a unit vector, if
A) $m = \pm 1$
B) $m = |\overrightarrow{\mathbf{a}}|$
C) $m = \frac{1}{|\overrightarrow{\mathbf{a}}|}$
D) $m = \pm \ 2$
Explanation
(c)
Since, $m\ \overrightarrow{\mathbf{a}}$ is a unit vector, if and only, if
$\left| m\ \overrightarrow{\mathbf{a}} \right| = 1\ \Rightarrow |m\ |\left| \overrightarrow{\mathbf{a}} \right| = 1\ \Rightarrow m\left| \overrightarrow{\mathbf{a}} \right| = 1$
$\Rightarrow m = \frac{1}{|\overrightarrow{\mathbf{a}}|}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.