Question

If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.

Answer 1

Let the direction cosines of the line be l, m and n.

We know that l² + m² + n² = 1.

Let the line make angle θ with the positive direction of the z-axis.

α=90°, β=60°, γ=Θ

So, cos²90^°+cos²60^°+cos²θ=1