Question

Angle between two diagonal of the cube is ____

(A) cos^–1(1/√3)

(B) cos^–1(1/3)

(C) cos^–1(1/9)

(D) cos^–1(√3/2)

Answer 1

The correct option (B) cos^–1(1/3)

Explanation:

Let O is on vertex of cube and vector(OA, OB, OC) are directions with x, y, z axis.

also OA = OB = OC = a

diagonals are vector(AL, BM, CN,OP)

∴ vector AL = (– a, a, a)

vector BM = (a, – a, a)

Angle between vector AL & vector BM is θ

∴ cos θ = [vector(|AL ∙ BM|)/vector(|AL| |BM|)] = [{|– a² – a² + a²|}/{√(3a²) √(3a²)}]

∴ cosθ = (1/3) ⇒ θ = cos^–1(1/3).