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

$\begin{array}{1 1} (A) x = \pm \large\frac{1}{\sqrt 3} \\ (B) x = \pm \large\frac{1}{3} \\ (C) x = \pm 1 \\ (D) x = \pm 3\end{array} $

1 Answer

  • If $\overrightarrow a=a_1\hat i+a_2\hat j+a_3\hat k$
  • $|\overrightarrow a|=\sqrt{a_1^2+a_2^2+a_3^2}$
Step 1:
Let $\overrightarrow a=x(\hat i+\hat j+\hat k)$
$\qquad\;\;=x\hat i+x\hat j+x\hat k$
The magnitude of $\overrightarrow a$ is $|\overrightarrow a|=\sqrt{x^2+x^2+x^2}$
Step 2:
But it is given $\overrightarrow a$ is a unit vector.
Hence $|\overrightarrow a|=1$
$\Rightarrow x\sqrt 3=\pm 1$
Therefore $x=\pm\large\frac{1}{\sqrt 3}$
answered May 23, 2013 by sreemathi.v

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