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

The correct option is A $\pm \frac{1}{\sqrt{3}}$

$x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector.
$\Rightarrow \left|x\right(\hat{i}+\hat{j}+\hat{k}\left)\right|=1$
$\Rightarrow {\left|x\right(\hat{i}+\hat{j}+\hat{k}\left)\right|}^2=1$
$\Rightarrow x^2(1^2+1^2+1^2)=1$
$\Rightarrow 3x^2=1$
$\Rightarrow x=\pm \frac{1}{\sqrt{3}}$