Q65 / 150 · MHT CET 2019 (Shift 2) · Mathematics

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.

  • A
    91
  • B
    94
  • Correct answer
    C
    92
  • D
    93

Solution

We have
AB=5-3i^+-2-7j^+3-4k^
=2i^-9j^-k^
AC=-4-3i^+5-7j^+6-4k^
=-7i^-2j^+2k^
and AD=1-3i^+2-7j^+3-4k^
=-2i^-5j^-k^
∴ Volume of the parallelepiped with AB, AC and AD on the co-terminus edges
=ABACAD=2-9-1-7-22-2-5-1
=22+10+97+4-135-4
=212+911-131
=24+99-31
=92=92 cubic units

Hence, the correct answer is option: 'C'.

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