Find the direction cosines of a vector which is equally inclined to the x - axis, y - axis and z - axis.

Direction cosines of a vector l, m, n are related to each other as

Now given that equally inclined to three axes with an angle of θ. Then direction cosines l, m, n are

l = m = n = cosθ

Putting values of direction cosines in equation,

Cos²θ + Cos²θ + Cos²θ = 1

3Cos²θ = 1