JEE Main 2017MathematicsThree Dimensional GeometryMediumMCQ

JEE Main 2017 — Three Dimensional Geometry Question with Solution

JEE Main 2017 (09 Apr Online)

Question

If the line, x-31=y+2-1=z+λ-2 lies in the plane, 2x-4y+3z=2 , then the shortest distance between this line and the line, x-112=y9=z4 is

Choose an option

Show full solutionCorrect option: D
Correct answer
D0

Step-by-step explanation

The points 3, -2, -λ lie on Plane 2x-4y+3z-2=0

⇒6+8-3λ-2=0

⇒3λ=12

⇒λ=4

Now,

x-31=y+2-1=z+4-2.......i

x-112=y9=z4........ii

Shortest distance formula

d=x1-x2y2-y1z2-z1a1a2a3b1b2b3i^j^k^a1a2a3b1b2b3

Calculating we get the value as 0
Hence lines are intersecting (As b→∦d→ )

∴ Shortest distance =0

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Three Dimensional Geometry chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2017, 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.