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MHT CET202310 May 2023Evening ShiftMathematicsVector AlgebraActual

If the volume of tetrahedron, whose vertices are with position vectors i -6 j +10 k ,- i -3 j +7 k , 5 i - j + k and 7 i -4 j +7 k is 11 cubic units, then value of is

Options

  1. A4
  2. B5
  3. C7
  4. D6

Correct answer

C. 7

Step-by-step solution

aligned & Let a = i -6 j +10 k , & b =- i -3 j +7 k , & c =5 i - j + k , & d =7 i -4 j +7 k & AB =-2 i +3 j -3 k & AC =4 i +5 j +( -10) k & AD =6 i +2 j -3 k & Volume of tetrahedron = 1 6 [ array lll AB & AC & AD array ] & 11= 1 6 | array ccc -2 & 3 & -3 4 & 5 & -10 6 & 2 & -3 array | & 11= 1 6 -2(-15-2 +20)-3(-12-6 +60) & -3(8-30) & =7& aligned

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