Question

The value of $x$ if $x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector is

• A. $\pm \frac{1}{\sqrt{3}}$
• B. $\pm \sqrt{3}$
• C. $\pm 3$
• D. $\pm \frac{1}{3}$

Answer 1

Answer: (A)

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

If $x(\hat{i}+\hat{j}+\hat{k})$ is an unit vector then

$|x(\hat{i}+\hat{j}+\hat{k})|=1$

$\Rightarrow |x\sqrt{1^2+1^2+1^2}|=1$

$\Rightarrow \sqrt{3}|x|=1$

$\Rightarrow |x|=\frac{1}{\sqrt{3}}$

$\therefore x=\pm \frac{1}{\sqrt{3}}$