The angle between a principal diagonal of a cube and a diagonal of its face is:

The angle between a principal diagonal of a cube and a diagonal of its face is:

• A. cos⁻¹(√(2/3))
• B. cos⁻¹(1/3)
• C. cos⁻¹(1/√3)
• D. 45°

Answer: A) cos⁻¹(√(2/3))

Explanation: Principal diagonal DRs: 1, 1, 1. Face diagonal DRs: 1, 1, 0. cos θ = |(1)(1) + (1)(1) + (1)(0)| / (√(3) * √(2)) = 2 / √(6) = √(4/6) = √(2/3). θ = cos⁻¹(√(2/3)).