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JEE Main202310 Apr 2023Morning ShiftMathematicsVector AlgebraActual

Let O be the origin and the position vector of the point P be - i ^ - 2 j ^ + 3 k . If the position vectors of the points A , B and C are - 2 i ^ + j ^ - 3 k , 2 i ^ + 4 j ^ - 2 k and - 4 i ^ ^ + 2 j ^ - k respectively, then the projection of the vector O P → on a vector perpendicular to the vectors A B → and A C → is

Options

  1. A3
  2. B8 3
  3. C7 3
  4. D10 3

Correct answer

A. 3

Step-by-step solution

Given, O be the origin and the position vector of the point P be - i ^ - 2 j ^ + 3 k ^ , So, O P → = - i ^ - 2 j ^ + 3 k ^ Also given the position vectors of the points A ,   B and C are - 2 i ^ + j ^ - 3 k ^ ,   2 i ^ + 4 j ^ - 2 k ^ and - 4 i ^ ^ + 2 j ^ - k ^ Now finding, A B → = 4 i ^ + 3 j ^ + k ^ A C → = - 2 i ^ + j ^ + 2 k ^ And A B → × A C → = i ^ j ^ k ^ 4 3 1 - 2 1 2 ⇒ A B → × A C → = 5 i ^ - 10 j ^ + 10 k ^ Now finding the Projection of

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