Question

The value of x if \(\rm x(\widehat i + \widehat j + \widehat k)\) is a unit vector is
1. \( \pm \frac{1}{3}\)
2. ± 3
3. \(\pm \sqrt 3\)
4. \( \pm \frac{1}{{\sqrt 3 }}\)

Answer 1

Correct Answer - Option 4 : \( \pm \frac{1}{{\sqrt 3 }}\)

Concept:

The modulus of a unit vector \(\rm \hat A\) = \(\rm |\hat A|\) = 1

Calculation:

Let \(\rm \vec A\) = \(\rm x(\widehat i + \widehat j + \widehat k)\)

\(\rm \vec A\) = \(\rm x\widehat i + x\widehat j + x\widehat k\)

Given:  \(\rm x(\widehat i + \widehat j + \widehat k)\) is a unit vector

So, \(\rm |\vec A| =1\)

\(\rm \sqrt{x^2 + x^2 + x^2} = 1\)

\(\rm \sqrt{3x^2 } = 1\)

|x|\(\rm \sqrt{3} = 1\)

|x| = \(1\over\sqrt3\)

x = \(\boldsymbol{\pm{1\over\sqrt3}}\)