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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

Consider the line L ≡ x - 1 2 = y + 2 3 = z - 7 6 . Point P 2 , - 5,0 and Q are such that P Q is perpendicular to the line L and the midpoint of P Q lies on line L , then coordinates of Q are

Options

  1. A- 4 , - 5 , 2
  2. B- 3,0 , 1
  3. C1,6 , 2
  4. D1,5 , 7

Correct answer

A. - 4 , - 5 , 2

Step-by-step solution

Q is reflection of P about line L Coordinate of point R are 2 λ + 1,3 λ - 2,6 λ + 7 P R → = 2 λ - 1,3 λ + 3,6 λ + 7 From diagram P R → ⋅ 2 i ^ + 3 j ^ + 6 k ^ = 0 4 λ - 2 + 9 λ + 9 + 36 λ + 42 = 0 49 λ + 49 = 0 ⇒ λ = - 1 So, coordinates of R are - 1 , - 5 , 1 ⇒ coordinates of Q are - 4 , - 5 , 2

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