JEE Main 2017MathematicsThree Dimensional GeometryHardMCQ

JEE Main 2017 — Three Dimensional Geometry Question with Solution

JEE Main 2017 (09 Apr Online)

Question

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B & C, then the locus of the centroid of ΔABC is

Choose an option

Show full solutionCorrect option: A
Correct answer
A1x2+1y2+1z2=1

Step-by-step explanation

Let centroid be h, k, l

x-intercept=3h 

y-intercept=3k

and z-intercept=3l

Now, the equation of plane is x3h+y3k+z3l=1.

Distance from 0, 0, 0

⇒119h2+19k2+19l2=3

⇒1x2+1y2+1z2=1

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.