If $x(\hat{i}+\hat{j}+\hat{k})$ is a uni

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If $x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector then value of x is :

Options:

$±\sqrt{3}$

$±\frac{1}{3}$

±3

$±\frac{1}{\sqrt{3}}$

Correct Answer:

$±\frac{1}{\sqrt{3}}$

Explanation:

$x(\hat{i}+\hat{j}+\hat{k}) = \vec{y}$

so $|\vec{y}| = 1$

⇒ $\sqrt{x^2+x^2+x^2} = 1$

so $\sqrt{3 x^2} = 1$

so $x = ±\frac{1}{\sqrt{3}}$