Question

Can a vector have direction angles 45° , 60° , 120°.

Answer 1

We know that, If l, m, n are the direction cosine of a vector and α, β, γ are the direction angle, then

– l = cosα, m = cosβ, n = cosγ

And, l² + m² + n² = 1 …… (i)

∴ l = cos45°, m = cos60°, n = cos120°

l = \(\cfrac 1{\sqrt2}\), m = \(\cfrac12\), n = \(-\cfrac12\)

Now, substituting l, m, n in equation (i), we get -

⇒ L.H.S = R.H.S

∴ A vector can have direction angles 45° , 60° , 120°.