Question

A line makes angles α, β, γ with the co-ordinate axes and α + β = 90°, then γ = ______.

Options

• 30°

• 90°

• 60°

• 45°

Answer 1

A line makes angles α, β, γ with the co-ordinate axes and α + β = 90°, then γ = 90°.

Explanation:

A line makes angles α, β, γ with the co-ordinate axes and α + β = 90°

∴ cos² α + cos² β + cos² γ = 1

⇒ cos² α + cos² (90 - α) + cos² γ = 1 

⇒ cos² α + sin² α + cos² γ = 1

⇒ 1 + cos² γ = 1

⇒ cos² γ = 0

⇒ γ = 90°