JEE Main 2021MathematicsThree Dimensional GeometryMediumNumerical

JEE Main 2021 — Three Dimensional Geometry Question with Solution

JEE Main 2021 (26 Aug Shift 2)

Question

Let Q be the foot of the perpendicular from the point P(7,-2,13) on the plane containing the lines x+16=y-17=z-38 and x-13=y-25=z-37
Then (PQ)2, is equal to ______.

Enter your answer

Show full solutionCorrect answer: 96
Correct answer
96

Step-by-step explanation

Equation of the plane

A(x+1)+B(y-1)+C(z-3)=0

where 6 A+7 B+8C=0 and 3 A+5 B+7C=0

By cross multiplication method, we get

A1=B-2=C1

⇒1(x+1)-2(y-1)+1(z-3)=0⇒x-2y+z=0

Let Q(α,β,γ)

α-71=β+2-2=γ-131=-(7+4+13)1+4+1=-4

Q(α,β,γ)=Q(3,6,9)

PQ=7-32+-2-62+13-92

(PQ)2=16+64+16

(PQ)2=96

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About this question

This is a previous-year question from JEE Main 2021, 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.