JEE Main 2019MathematicsThree Dimensional GeometryEasyMCQ

JEE Main 2019 — Three Dimensional Geometry Question with Solution

JEE Main 2019 (12 Apr Shift 1)

Question

If the line x-23=y+12=z-1-1 intersects the plane 2x+3y-z+13=0 at a point P and the plane 3x+y+4z=16 at a point Q, then PQ is equal to

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Show full solutionCorrect option: C
Correct answer
C214

Step-by-step explanation

x-23=y+12=z-1-1=λ
x=3λ+2, y=2λ-1, z=-λ+1
Intersection with plane 2x+3y-z+13=0
Hence, 23λ+2+32λ-1--λ+1+13=0
13λ+13=0
λ=-1
∴ P-1,-3,2
Intersection with plane 3x+y+4z=16
Hence, 33λ+2+2λ-1+4-λ+1=16
λ=1
Q5,1,0
PQ=62+42+22=56=214

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About this question

This is a previous-year question from JEE Main 2019, covering the Three Dimensional Geometry chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.