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JEE Advanced2013MathematicsVector AlgebraActual

Let PR → = 3 i ⁡ ^ + j ⁡ ^ - 2 k ^ and SQ → = i ⁡ ^ - 3 j ⁡ ^ - 4 k ^ determine diagonals of a parallelogram PQRS and PT → = i ⁡ ^ + 2 j ⁡ ^ + 3 k ^ be another vector. Then the volume of the parallelepiped determined by the vectors PT → , PQ → and PS → is

Options

  1. A5
  2. B20
  3. C10
  4. D30

Correct answer

C. 10

Step-by-step solution

PR → = PQ → + PS → SQ → = PQ → - PS → PS → = PR → - SQ → 2 PQ → = PR → + SQ → 2 V = PQ → PS → PT → V = 1 4 PR → + SQ → , PR → - SQ → , PT → V = 1 2 PR → , SQ → , PT → V = 1 2 3 1 - 2 1 - 3 - 4 1 2 3 V = 1 2 - 3 - 7 - 1 0 = 1 0

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