JEE Main 2022MathematicsThree Dimensional GeometryEasyNumerical

JEE Main 2022 — Three Dimensional Geometry Question with Solution

JEE Main 2022 (24 Jun Shift 1)

Question

If the shortest distance between the lines r→=-i^+3k^+λi^-aj^ and r→=-j^+2k^+μi^-j^+k^ is 23, then the integral value of a is equal to _____

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

D.R. 's of a→1=-1,0,3

D.R. 's of a→2=0,-1,2

D.R. 's of b→1=1,-a,0 

D.R. 's of b→2=1,-1,1 

Now, a→2-a→1=i^-j^-k^

and b→1×b→2=i^j^k^1-a01-11

b→1×b2→=i^-a-j^+k^a-1

i.e. b1→×b2→=a2+1+a-12

So, a→2-a→1·b→1×b→2=2-2a

Shortest distance between the lines, 21-aa2+1+a-12=23

Squaring on both the sides, we get,

31-a2=a2-a+1

 i.e. a=2,12

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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.