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MHT CET2019Evening ShiftMathematicsVector AlgebraActual

If A, B, C and D are 3,7 , 4 , 5 , - 2 , - 3 , - 4,5 , 6 and 1,2 , 3 respectively, then the volume of the parallelepiped with AB, AC and AD as the co-terminus edges, is ….cubic units.

Options

  1. A91
  2. B94
  3. C92
  4. D93

Correct answer

C. 92

Step-by-step solution

We have A B = 5 - 3 i ^ + - 2 - 7 j ^ + 3 - 4 k ^ = 2 i ^ - 9 j ^ - k ^ A C = - 4 - 3 i ^ + 5 - 7 j ^ + 6 - 4 k ^ = - 7 i ^ - 2 j ^ + 2 k ^ and A D = 1 - 3 i ^ + 2 - 7 j ^ + 3 - 4 k ^ = - 2 i ^ - 5 j ^ - k ^ ∴ Volume of the parallelepiped with AB, AC and AD on the co-terminus edges = A B A C A D = 2 - 9 - 1 - 7 - 2 2 - 2 - 5 - 1 = 2 2 + 10 + 9 7 + 4 - 1 35 - 4 = 2 12 + 9 11 - 1 31 = 24 + 99 - 31 = 92 = 92 cubic units

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