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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

A line L lies in the plane 2 x - y - z = 4 such that it is perpendicular to the line x - 2 2 = y - 3 1 = z - 4 5 . The line L passes through the point of intersection of the given line and given plane. Which of the following points does not satisfy line L ?

Options

  1. A- 5 , - 1 2 , - 27 2
  2. B3 , 1 , 6
  3. C0 , 29 2 , - 37 2
  4. D- 4 , 5 2 , - 29 2

Correct answer

B. 3 , 1 , 6

Step-by-step solution

Any point on given line is 2 λ + 2 , λ + 3,5 λ + 4 This must satisfy the equation of the plane ⇒ 4 λ + 4 - λ - 3 - 5 λ - 4 = 4 ⇒ - 2 λ = 7 ⇒ λ = - 7 2 So, the coordinates of point are - 5 , - 1 2 , - 27 2 A normal vector to given plane n → = 2 i ^ - j ^ - k ^ A vector parallel to given line b → = 2 i ^ + j ^ + 5 k ^ A vector parallel to required line i ^ j ^ k ^ 2 - 1 - 1 2 1 5 = i ^ - 4 - j ^ 12 + k ^ 4 = - 4 i ^ + 3 j ^ - k ^ Equation of required line is x + 5 1 = y + 1 2 3 = z + 27 2 - 1

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