Published by:
CGP EDU Academic Team
Published on: August 13, 2026
A line makes angles α α , β β , γ γ , δ δ with the four diagonals of a cube. Then cos 2 α α + cos 2 β β + cos 2 γ γ + cos 2 δ δ is equal to
Text Solution
Verified by ExpertsThe correct answer is:
B
The direction ratios of the diagonal are (1, 1, 1). ⇒⇒ direction cosine are . Similarly direction cosine of are and those of and are |
.
Let l, m, n be direction cosines of the line so that
cos α α = 
, cos β β = 
, cos γ γ = 
,
cos δ δ = 
⇒ ⇒ cos 2 α α + cos 2 β β + cos 2 γ γ + cos 2 δ δ = 
= 
(since l 2 + m 2 + n 2 = 1)
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