Question

If $\overrightarrow{a}$ is a non-zero vector of magnitude $a$ and $\lambda ,$ a non-zero scalar, then $\lambda \overrightarrow{a}$ is a unit vector if:

• A. $\lambda =1$
• B. $\lambda =-1$
• C. $a=|\lambda |$
• D. $a=\frac{1}{|\lambda |}$

Answer 1

The correct option is D $a=\frac{1}{|\lambda |}$

$\overrightarrow{a}$ is a non-zero vector of magnitude $a$
$\Rightarrow |\overrightarrow{a}|=a$
Now, $\lambda \overrightarrow{a}$ is a unit vector if $|\lambda \overrightarrow{a}|=1$ or $|\lambda ||\overrightarrow{a}|=1$
$\Rightarrow |\lambda |a=1\Rightarrow a=\frac{1}{|\lambda |}$