JEE Main 2021MathematicsThree Dimensional GeometryMediumMCQ

JEE Main 2021 — Three Dimensional Geometry Question with Solution

JEE Main 2021 (16 Mar Shift 2)

Question

If the foot of the perpendicular from point 4,3,8 on the line L1:x-al=y-23=z-b4, l≠0 is 3,5,7, then the shortest distance between the line L1 and line L2:x-23=y-44=z-55 is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B16

Step-by-step explanation

3,5,7 satisfy the line L1

3-aℓ=5-23=7-b4

3-aℓ=1 & 7-b4=1

a+ℓ=3 …1 & b=3 ...2

v→1=4,3,8-3,5,7

v→1=1,-2,1

v→2=ℓ,3,4

v→1·v→2=0⇒ℓ-6+4=0⇒ℓ=2

a+ℓ=3⇒a=1

L1:x-12=y-23=z-34

L2:x-23=y-44=z-55

A=1,2,3

B=2,4,5

AB→=1,2,2

p→=2i^+3j^+4k^

q→=3i^+4j^+5k^

p→×q→=-i^+2j^-k^

Shortest distance =AB→·p→×q→p→×q→=16

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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.