Question

If a vector makes angles α, β, γ with OX, OY and OZ respectively, then write the value of sin²α + sin²β + sin²γ.

Answer 1

The sum of squares of direction cosines of a vector is 1.

Let the angles made by vector be α, β, γ.

Then, we get cos²α+cos²β+cos²γ=1

using cos²θ=1 - sin²θ, we get

(1 - sin²α) +(1 - sin²β) + (1 - sin²γ) = 1

Or, sin²α + sin²β + sin²γ = 2