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JEE Main2017MathematicsVector AlgebraActual

The area (in sq. units) of the parallelogram whose diagonals are along the vectors 8 i ^ - 6 j ^ and 3 i ^ + 4 j ^ - 12 k ^ , is:

Options

  1. A20
  2. B65
  3. C52
  4. D26

Correct answer

B. 65

Step-by-step solution

Let the given diagonals be d 1 → and d 2 → , then d 1 × d 2 = i ^ j ^ k ^ 8 - 6 0 3 4 - 12 = 72 i ^ - - 96 j ^ + 50 k ^ d 1 × d 2 = 72 2 + - 96 2 + 50 2 = 5184 + 9216 + 2500 d 2 × d 2 =   16900 = 130 Area = 1 2 d 1 × d 2 = 1 2 × 130 = 65

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