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Question: Answered & Verified by Expert
A plane P contains the line x+2y+3 z+1=0=x-y-z-6, and is perpendicular to the plane -2x+y+z+8=0. Then which of the following points lies on P?
MathematicsThree Dimensional GeometryJEE MainJEE Main 2021 (26 Aug Shift 1)
Options:
  • A (2,-1,1)
  • B (0,1,1)
  • C (-1,1,2)
  • D (1,0,1)
Solution:
1330 Upvotes Verified Answer
The correct answer is: (0,1,1)

A plane which containing the line

x+2y+3z+1=0=x-y-z-6 is

x+2y+3z+1+λx-y-z-6=0

(1+λ)x+(2-λ)y+(3-λ)z+1-6λ=0

This plane is perpendicular to the plane -2x+y+z+8=0 then

-2(1+λ)+1(2-λ)+1(3-λ)=0

λ=34

Equation of plane is

74x+54y+94z=144

7x+5y+9z=14

Clearly, (0,1,1) lies on the plane.

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