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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

A line L passing through 1,2 , 3 and perpendicular to the line L 1 : x - 1 - 2 = y + 1 3 = z - 5 4 is also intersecting the line L 1 . If line L intersects the plane 2 x + y + z + 6 = 0 at point α , β , γ , then the value of 2020 α + β + 2 γ is equal to

Options

  1. A2058
  2. B78
  3. C28
  4. D- 4012

Correct answer

C. 28

Step-by-step solution

Given, L 1 : x - 1 - 2 = y + 1 3 = z - 5 4 Let, b → = - 2 i ^ + 3 j ^ + 4 k ^ (a vector parallel to the line) From diagram coordinates of point are B - 2 λ + 1,3 λ - 1,4 λ + 5 Now, DR's of A B → = < - 2 λ , 3 λ - 3,4 λ + 2 > A B → ⋅ b → = 0 ⇒ 4 λ + 9 λ - 9 + 16 λ + 8 = 0 ⇒ 29 λ = 1 ⇒ λ = 1 29 A B → = - 2 i ^ 29 - 84 j ^ 29 + 62 k ^ 29 So, the equation of line L is x - 1 1 = y - 2 42 = z - 3 - 31 Any general point on this line is λ + 1,42 λ + 2 , - 31 λ + 3 This must satisfy the equation of the plane ⇒ 2 λ + 2 + 42

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