If a line makes angle with x-axis and y-axis respectively, then the angle made by the line with z-axis is

If a line makes angles α , β and γ with the axes then,

cos²α + cos²β + cos²γ = 1 → (1)

Here,

α

β

Now,

cos²α + cos²β + cos²γ = 1

cos² + cos² + cos²γ = 1

+ + cos²γ = 1

+ cos²γ = 1

cos²γ = 1 -

cos²γ

cosγ

γ