Question

If $\overrightarrow{a}$ is a non-zero vector of modulus $a$ and $m$ is a non-zero scalar, then $m\overrightarrow{a}$ is a unit vector if

• A. $m=\pm 1$
• B. $a=|m|$
• C. $a=\frac{1}{|m|}$
• D. $a=\frac{1}{m}$

Answer 1

Answer: (C)

$a=\frac{1}{|m|}$

$m\overrightarrow{a}$ is a unit vector if and only if
$|m\overrightarrow{a}|=1$

$\Rightarrow |m||\overrightarrow{a}|=1$

$\Rightarrow |m|a=1$

$\Rightarrow \frac{1}{|m|}$