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MHT CET202525 Apr 2025Morning ShiftMathematicsVector AlgebraActual

The position vectors of the points A, B, C are i +2 j - k , i + j + k , 2 i +3 j +2 k respectively. If A is chosen as the origin, then the cross product of position vectors of B and C are

Options

  1. A-5 i +2 j + k
  2. B- i +0 j - k
  3. Ci - k
  4. D5 i -2 j - k

Correct answer

A. -5 i +2 j + k

Step-by-step solution

Given position vectors: r _A = i + 2 j - k r _B = i + j + k r _C = 2 i + 3 j + 2 k With A as the origin, the position vectors relative to A are: AB = r _B - r _A = (1-1) i + (1-2) j + (1-(-1)) k = - j + 2 k AC = r _C - r _A = (2-1) i + (3-2) j + (2-(-1)) k = i + j + 3 k The cross product is evaluated as: AB AC = vmatrix i & j & k 0 & -1 & 2 1 & 1 & 3 vmatrix = i (-3 - 2) - j (0 - 2) + k (0 - (-1)) = -5 i + 2 j + k This result corresponds exactly with option A. Final answer: A

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