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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

1 Answer

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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).

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