Question

Find the value of $x$ for which$x(\hat{i}+\hat{j}+\hat{k})$is a unit vector.

Answer 1

$x(\hat{i}+\hat{j}+\hat{k})$is a unit vector if $|x(\hat{i}+\hat{j}+\hat{k})|=1$
Now,
$|x(\hat{i}+\hat{j}+\hat{k})|=1$
$⇒\sqrt{x^{2}+x^{2}+x^{2}}=1$
$⇒\sqrt{3x^{2}}=1$
$⇒\sqrt{3}x=1$
$⇒x=\pm\frac{1}{\sqrt{3}}$
Hence,the required value of $x$ is $\pm\frac{1}{\sqrt{3}}.$