Question

If $\overrightarrow{a}=2\hat{i}+2\hat{j}-\hat{k}$ and $|x\overrightarrow{a}|=1$, then $x$ is equal to

• A. $\pm \frac{1}{3}$
• B. $\pm \frac{1}{4}$
• C. $\pm \frac{1}{5}$
• D. $\pm \frac{1}{6}$

Answer 1

Answer: (A)

$\pm \frac{1}{3}$

$|x\overrightarrow{a}|=1$
$\to$
$|x||\overrightarrow{a}|=1$
$\Rightarrow |x|=\frac{1}{|\overrightarrow{a}|}$
$\Rightarrow |x|=\frac{1}{\sqrt{2^2+2^2+1}}$
$\Rightarrow |x|=\frac{1}{3}$