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MHT CET202312 May 2023Evening ShiftMathematicsVector AlgebraActual

If the volume of tetrahedron, whose vertices are A (1,2,3), B (-3,-1,1), C (2,1,3) and D (-1,2, x) is 11 6 cubic units, then the value of x is

Options

  1. A3
  2. B-2
  3. C4
  4. D-1

Correct answer

C. 4

Step-by-step solution

aligned & AB =-4 i -3 j -2 k & AC = i - j & AD =-2 i +(x-3) k & Volume = 1 6 | array ccc -4 & -3 & -2 1 & -1 & 0 -2 & 0 & x-3 array | & 11=4(x-3)+3(x-3)-2(-2) & 11=7 x-17 aligned

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