Question

If α, β, γ are direction angles of a line and α = 60°, β = 45°, then γ = ______.

Options

• 30° or 90°

• 45° or 60°

• 90° or 130°

• 60° or 120°

Answer 1

If α, β, γ are direction angles of a line and α = 60°, β = 45°, γ = 60° or 120°.

Explanation:

We have 

cos²α + cos²β + cos²γ = 1

⇒ cos²60° + cos²45° + cos²γ = 1

⇒ `(1/2)^2 + (1/sqrt2)^2 + cos^2 gamma = 1`

⇒ `1/4 + 1/2 + cos^2 gamma = 1`

⇒ `cos^2 gamma = 1 - 3/4 = 1/4`

⇒ `cos gamma = +- 1/2`

⇒ γ = 60° or 120°