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JEE Main202124 Feb 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The vector equation of the plane passing through the intersection of the planes r → · i ^ + j ^ + k ^ = 1 and r → · i ^ - 2 j ^ = - 2 , and the point 1 , 0 , 2 is:

Options

  1. Ar → · i ^ + 7 j ^ + 3 k ^ = 7
  2. Br → · i ^ - 7 j ^ + 3 k ^ = 7 3
  3. Cr → · i ^ + 7 j ^ + 3 k ^ = 7 3
  4. Dr → · 3 i ^ + 7 j ^ + 3 k ^ = 7

Correct answer

A. r → · i ^ + 7 j ^ + 3 k ^ = 7

Step-by-step solution

r → · i ^ + j ^ + k ^ = 1 r → · i ^ - 2 j ^ = - 2 point 1 ,   0 ,   2 E q n of plane r → · i ^ + j ^ + k ^ - 1 + λ r → · i ^ - 2 j ^ + 2 = 0 r → · i ^ 1 + λ + j ^ 1 - 2 λ + k ^ 1 - 1 + 2 λ = 0 Point i ^ + 0 j ^ + 2 k ^ = r → ∴ i ^ + 2 k ^ · i ^ 1 + λ + j ^ 1 - 2 λ + k ^ 1 - 1 + 2 λ = 0 1 + λ + 2 - 1 + 2 λ = 0 λ = - 2 3 ∴ r → · i ^ 1 3 + j ^ 7 3 + k ^ = 7 3 r → &#

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