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MHT CET202617 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

The angle between a diagonal and one of its edges of a cube is ...................

Options

  1. A⁻¹ ( 1 2 )
  2. B⁻¹ ( 1 3 )
  3. C⁻¹ ( 1 2 2 )
  4. D⁻¹ ( 2 )

Correct answer

D. ⁻¹ ( 2 )

Step-by-step solution

Consider a cube of side length a with one of its vertices at the origin (0,0,0) and edges along the coordinate axes. The vector representing an edge along the x-axis is e = a i . The vector representing the diagonal of the cube from the origin is d = a i + a j + a k . The angle between the diagonal and the edge is given by = d e | d | | e | . d e = (a)(a) + (a)(0) + (a)(0) = a^2 | d | = a^2 + a^2 + a^2 = a 3 | e | = a = a^2 a 3 a = 1 3 Using trigonometric identities, if = 1 3 , then the adjacent side is 1 and the h

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