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JEE Main20198 Apr 2019Morning ShiftMathematicsVector AlgebraActual

The magnitude of the projection of the vector 2 i ^ + 3 j ^ + k ^ on the vector perpendicular to the plane containing the vectors i ^ + j ^ + k ^ and i ^ + 2 j ^ + 3 k ^ , is:

Options

  1. A3 6
  2. B3 2
  3. C6
  4. D3 2

Correct answer

B. 3 2

Step-by-step solution

Vector perpendicular to i ^ + j ^ + k ^ and i ^ + 2 j ^ + 3 k ^ = i ^ j ^ k ^ 1 1 1 1 2 3 = i ^ - 2 j ^ + k ^ ∴ Required projection = | ( 2 i ^ + 3 j ^ + k ^ ) ⋅   ( i ^ - 2 j ^ + k ^ ) | | i ^ - 2 j ^ + k ^ | = | 2 - 6 + 1 | 6 = 3 6 = 3 2

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