the vector u makes angles α(alpha), β(beta), γ(gama) with respectively the X–axis, the Y –axis and the Z–axis. Find γ if α = 2π/3 and β = π /4

Answer 1

This question deals with direction cosines

you must have come across the property
cos^2 α + cos^2 β + cos^2 γ = 1
cos^2 (2π/3) + cos^2 (π/4) + cos^2 γ = 1
1/4 + 1/2 + cos^2 γ = 1
cos^2 γ = 1 - 1/2 - 1/4
cos^2 γ = 1/4
cos γ = 1/2
γ = π/6 using only the first quadrant case