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The cosine of angle between any two diagonals of a cube is (A) 1/3 (B) ½ (C) 2/3 (D) 1/root3

The cosine of angle between any two diagonals of a cube is
(A) 1/3
(B) ½
(C) 2/3
(D) 1/root3

Grade:11

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
The angle between 2 face diagonals will be 90 as the face is a square(a rhombus).So, cos of that angle will be 0.

If you consider a face diagnol and a body diagonal at any vertex of the cube, then it will be a right angled triangle with sides a, a(2)1/2and a(3)1/2. with a being the side of the cube and will be opposite to the angle between the face diagonal and the body diagonal.

If you consider both the body diagonals of the cube, then it will be a triangle with sides a, a(3)1/2/2and a(3)1/2/2. with a being the side of the cube and will be opposite to the angle between the 2 diagonals . In that case, use cosine law to find the cos of angle between the 2 body diagonals.

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