Question

A line makes angles α, β, γ and δ with the four diagonals of a cube, then cos²α + cos²β + cos²γ + cos²δ = 

(A) 1

(B) 4/3

(C) 3/4 

(D) 4/5

Answer 1

Answer is (B) 4/3

See Fig.

The direction ratios of the diagonal vector OR  are (1, 1, 1).

Direction cosine are (1/√3, 1/√3, 1/√3).

Similarly, direction cosine of vector AS are (1/√3, -1/√3, - 1/√3)

and vector BP are (1/√3, 1/√3, - 1/√3).