Find the direction cosines of a line which makes equal angles with the coordinate axes.

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

l^{2} + m ^{2} + n^{2} = 1

cos^{2} α + cos^{2}β + cos^{2}γ = 1

From 1 we have

cos^{2} α + cos^{2} α + cos^{2} α = 1

3 cos^{2} α = 1

The direction cosines are

2