JEE Main 2022MathematicsThree Dimensional GeometryEasyMCQ

JEE Main 2022 — Three Dimensional Geometry Question with Solution

JEE Main 2022 (25 Jun Shift 1)

Question

Let Q be the mirror image of the point P1,0,1 with respect to the plane S:x+y+z=5. If a line L passing through 1,-1,-1, parallel to the line PQ meets the plane S at R, then QR2 is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B5

Step-by-step explanation

Let parallel vector of L=

Let Qa,b,c

As Q is the mirror image on given plane x+y+z=5

so a-11=b-01=c-11=-22-53

a=3,b=2,c=3

i.e. Q≡3,2,3

Let the vector parallel to L be b→

So, b→=1,1,1

Equation of line L:x-11=y+11=z+11

Let point Rλ+1,λ-1,λ-1 is lying on plane x+y+z=5, so, 3λ-1=5

⇒λ=2
So, point R is 3,1,1

Hence, QR2=5

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About this question

This is a previous-year question from JEE Main 2022, 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.