KCET · Maths · Vector Algebra
The value of if \( x(\hat{i}+\hat{j}+\hat{k}) \) is a unit vector is
- A \( \pm \frac{1}{\sqrt{3}} \)
- B \( 0 \pm \sqrt{3} \)
- C \( \pm 3 \)
- D \( \pm \frac{1}{3} \)
Answer & Solution
Correct Answer
(A) \( \pm \frac{1}{\sqrt{3}} \)
Step-by-step Solution
Detailed explanation
Given that, \( |x(i+j+k)|=1 \)
\[
\begin{array}{l}
\Rightarrow|x||\hat{i}+\hat{j}+\hat{k}|=1 \\
\Rightarrow|x| \sqrt{1+1+1}=1 \\
\Rightarrow|x| \sqrt{3}=1 \Rightarrow x=\pm \frac{1}{\sqrt{3}}
\end{array}
\]
\[
\begin{array}{l}
\Rightarrow|x||\hat{i}+\hat{j}+\hat{k}|=1 \\
\Rightarrow|x| \sqrt{1+1+1}=1 \\
\Rightarrow|x| \sqrt{3}=1 \Rightarrow x=\pm \frac{1}{\sqrt{3}}
\end{array}
\]
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