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MHT CET202411 May 2024Morning ShiftMathematicsVector AlgebraActual

If the volume of tetrahedron whose vertices are A (1,-6,10), B (-1,-3,7), C (5,-1, k ) and D (7,-4,7) is 11 cu . units, then the value of k is

Options

  1. A7
  2. B5
  3. C3
  4. D1

Correct answer

A. 7

Step-by-step solution

aligned Let a & = i -6 j +10 k , b & =- i -3 j +7 k , c & =5 i - j + k k , ~d & =7 i -4 j +7 k AB & =-2 i +3 j -3 k AC & =4 i +5 j +(k-10) k AD & =6 i +2 j -3 k aligned aligned & Volume of tetrahedron = 1 6 [ array lll AB & AC & AD array ] & 11= 1 6 | array ccc -2 & 3 & -3 4 & 5 & k -10 6 & 2 & -3 array | & 11= 1 6 -2(-15-2 k +20)-3(-12-6 k +60) & k =7 aligned

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