Find the value of \(x\) for which\( x(\hat{i}+\hat{j}+\hat{k})\)is a unit vector.
Find the value of \(x\) for which\( x(\hat{i}+\hat{j}+\hat{k})\)is a unit vector.
Solution and Explanation
\(x(\hat{i}+\hat{j}+\hat{k})\)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 \(\pm\frac{1}{\sqrt{3}}.\)
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