Question

If α, β and Δ are the angles made by a vectors with X, Y and Z – axes find the value of sin² α + sin² β + sin² Δ.

Answer 1

Answer:

consider ∆ = γ in this case.

$\large\rm { cos²α + cos²β + cos² γ = 1}$ .....(1)

$\large\rm { 1 - sin²α + 1 - sin²β + 1 - sin²γ = 1}$ .....(2)

Equating (1)&(2) ,

$\large\rm {sin² α + sin² β + sin² γ = 2}$

∴ $\large\rm { sin² α + sin² β + sin² ∆ = 2}$