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JEE Main202125 Feb 2021Evening ShiftMathematicsThree Dimensional GeometryActual

A plane passes through the points A 1 , 2 , 3 , B 2 , 3 , 1 and C 2 , 4 , 2 . If O is the origin and P is 2 , - 1 , 1 , then the projection of O P → on this plane is of length:

Options

  1. A2 5
  2. B2 7
  3. C2 3
  4. D2 11

Correct answer

D. 2 11

Step-by-step solution

Normal to plane n → = i ^ j ^ k ^ 1 1 - 2 0 1 1 = 3 i ^ - j ^ + k ^ O P → = 2 i ^ - j ^ + k ^ cos θ = 6 + 1 + 1 6 11 = 8 66 ⇒ sin θ = 2 66 ∴ Projection of O P → on plane = | O P → | sin θ = 2 11 option 4

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