imo class 12 three dimensional geometry

If a line makes angles α, β, γ, δ with the four diagonals of a cube, then cos²α + cos²β + cos²γ + cos²δ equals:

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If a line makes angles α, β, γ, δ with the four diagonals of a cube, then cos²α + cos²β + cos²γ + cos²δ equals:

  • A. 4/3
  • B. 3/4
  • C. 1
  • D. 2

Answer: A) 4/3

Explanation: Standard result in 3D geometry: If a line makes angles α, β, γ, δ with the four diagonals of a cube, the sum of their squared cosines is 4/3.

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