JEE Main 2018MathematicsThree Dimensional GeometryHardMCQ

JEE Main 2018 — Three Dimensional Geometry Question with Solution

JEE Main 2018 (15 Apr)

Question

A variable plane passes through a fixed point 3, 2, 1 and meets x, y and z-axes at A, B & C respectively. A plane is drawn parallel to the yz– plane through A, a second plane is drawn parallel to the zx- plane through B and a third plane is drawn parallel to the xy- plane through C. Then the locus of the point of intersection of these three planes, is

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Show full solutionCorrect option: A
Correct answer
A3x+2y+1z=1

Step-by-step explanation

Let plane be xa+yb+zc=1

It passes through 3,  2, 1.

∴3a+2b+1c=1

Now, A(a, 0, 0), B(0, b, 0), C(0, 0, c)

∴ Locus of point of intersection of planes x=a, y=b & z=c is 3x+2y+1z=1

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About this question

This is a previous-year question from JEE Main 2018, 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.