Find the value of x for which x ( i + j + k ) is a unit vector. - Vidyadip

Question

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

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Answer

We have, $\text{x}\big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\big)$ is a unit vector.
$\therefore\ \sqrt{\text{x}^2+\text{x}^2+\text{x}^2}=1$
$\Rightarrow\sqrt3|\text{x}|=1$
$\Rightarrow|\text{x}|=\frac{1}{\sqrt3}$
$\Rightarrow\text{x}=\pm\frac{1}{\sqrt3}$

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