Find the value of the given magnitude of the vector, \(\vec{a}=\frac{1}{{\sqrt 3}}\hat i + \frac{1}{{\sqrt 3}}\hat j + \frac{1}{{\sqrt 3}}\hat{k}\) ?

Question

Question

This question was previously asked in

AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 3)

Answer 1

Given:

\(\vec{a}=\frac{1}{{√ 3}}̂ i + \frac{1}{{√ 3}}̂ j + \frac{1}{{√ 3}}̂{k}\)

Formula:

The magnitude of vector aî + bĵ + ck̂ is given by √(a² + b² +c²)

Calculation:

Magnitude of \(\vec{a}=\frac{1}{{√ 3}}̂ i + \frac{1}{{√ 3}}̂ j + \frac{1}{{√ 3}}̂{k}\)

= √[(1/√3)2 + (1/√3)2 + (1/√3)2]

= 1