Question

If a line is inclined at 60° and 30° with the X and Y-axes respectively, then the angle which it makes with Z-axis is

(A) 0

(B) `pi/4`

(C) `pi/2`

(D) `pi/6`

Answer 1

Let α, β, γ be the angles made by a line with X, Y, Z axes respectively

∴ α = 60°, β = 30°

Since, cos²α + cos²β + cos²γ = 1

∴ cos² 60° + cos² 30° + cos² γ = 1

∴ `1/4 + 3/4 + cos^2 gamma = 1`

∴ `gamma = pi/2`