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KCET2014MathematicsMatrices

The angle between two diagonals of a cube is ( 30^ )

Options

  1. A( 30^ )
  2. B( 45^ )
  3. C( ⁻¹ ( 1 3 ) )
  4. D( ⁻¹ ( 1 3 ) )

Correct answer

C. ( ⁻¹ ( 1 3 ) )

Step-by-step solution

Consider a diagonal with each side ( 1 . ) Now, ( B C ) and ( O A ) are diagonals. So, Angle between diagonals = Angle between ( OA ) and ( BC ) ( OA =(1,1,1)-(0,0,0)=(1,1,1) ) ( BC =(0,1,1)-(1,0,0)=(-1,1,1) ) Now, [ array l = 1(-1)+1(1)+(1)(1) 1²+1²+1² (-1)²+1²+1² = 1 3 = ⁻¹ ( 1 3 ) array ]

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