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Question: Answered & Verified by Expert
Thevertices of a cubeare $(0,0,0),(2,0,$, 0), $(0,2,0),(0,0,2),(2,2,0),(2,0,2),(0,2,2),(2,2,2)$ respectively.
What is the angle between any two diagonals of the cube?
MathematicsThree Dimensional GeometryNDANDA 2010 (Phase 1)
Options:
  • A $\cos ^{-1}(1 / 2)$
  • B $\cos ^{-1}(1 / 3) \quad$
  • C $\cos ^{-1}(1 / \sqrt{3})$
  • D $\cos ^{-1}(2 / \sqrt{3})$
Solution:
2025 Upvotes Verified Answer
The correct answer is: $\cos ^{-1}(1 / 3) \quad$
Required angle $=\cos ^{-1}\left(\frac{1}{3}\right)$

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