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Question
Find the value of x for which \[x \left( \hat{i} + \hat{j} + \hat{k} \right)\] is a unit vector.
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Solution
We have, \[x \left( \hat{i} + \hat{j} + \hat{k} \right)\] is a unit vector.
\[\therefore \sqrt{x^2 + x^2 + x^2} = 1\]
\[ \Rightarrow \sqrt{3}\left| x \right| = 1\]
\[ \Rightarrow \left| x \right| = \frac{1}{\sqrt{3}}\]
\[ \Rightarrow x = \pm \frac{1}{\sqrt{3}}\]
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