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

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

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

$\sqrt{3x^2}=1$

$\sqrt{3}x=1$

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