Q114 / 180 · KCET 2016 · Mathematics

The value of if \( x(\hat{i}+\hat{j}+\hat{k}) \) is a unit vector is

  • Correct answer
    A
    \( \pm \frac{1}{\sqrt{3}} \)
  • B
    \( 0 \pm \sqrt{3} \)
  • C
    \( \pm 3 \)
  • D
    \( \pm \frac{1}{3} \)

Solution

Given that, \( |x(i+j+k)|=1 \)
\[ \begin{array}{l} \Rightarrow|x||\hat{i}+\hat{j}+\hat{k}|=1 \\ \Rightarrow|x| \sqrt{1+1+1}=1 \\ \Rightarrow|x| \sqrt{3}=1 \Rightarrow x=\pm \frac{1}{\sqrt{3}} \end{array} \]

Hence, the correct answer is option: 'A'.

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