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MHT CET202521 Apr 2025Morning ShiftMathematicsVector AlgebraActual

Three vectors i - k , i + j +(1- ) k and i + j +(1+ - ) k represents conterminus edges of a parallelopiped, then the volume of the parallelopiped depends on.

Options

  1. Aonly
  2. Bonly
  3. Cboth and
  4. Dneither nor

Correct answer

D. neither nor

Step-by-step solution

The volume of the parallelepiped is determined by the scalar triple product of the given vectors: a = (1, 0, -1) b = ( , 1, 1- ) c = ( , , 1+ - ) Evaluating the determinant: V = | vmatrix 1 & 0 & -1 & 1 & 1- & & 1+ - vmatrix | Expanding along the first row yields: V = | (1+ - - + ^2) - ( ^2 - ) | = | 1 | = 1 The volume simplifies to a constant value of 1, independent of both and . Therefore, the volume depends on neither parameter. Final answer: D

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