Question

The angle between any two diagonals of a cube is

• A. \(45^\circ\)
• B. \(60^\circ\)
• C. \(30^\circ\)
• D. \(\tan^{-1}(2\sqrt{2})\)

Hint:

Use dot product to find angle between lines in 3D.

Answer 1

The Correct Option is B

Step 1: Direction vectors of diagonals are \((1,1,1)\) and \((1,-1,1)\).
Step 2: \[ \cos\theta=\frac{1}{\sqrt{3}\sqrt{3}}=\frac{1}{3} \Rightarrow \theta=60^\circ \]