Let the direction cosines of the line making ∠ α with x-axis, β – with y axis and γ- with z axis are l, m and n

⇒ l = cos α, m = cos β and n = cos γ

Here given α = β = γ (line makes equal angles with the coordinate axes) ……….1

Direction Cosines are

⇒ l = cos α, m = cos β and n = cos γ

We have

l² + m ² + n² = 1

cos² α + cos²β + cos²γ = 1

From 1 we have

cos² α + cos² α + cos² α = 1

3 cos² α = 1

The direction cosines are