JEE Main 2016MathematicsThree Dimensional GeometryMediumMCQ

JEE Main 2016 — Three Dimensional Geometry Question with Solution

JEE Main 2016 (09 Apr Online)

Question

The distance of the point 1, -2, 4 from the plane passing through the point 1, 2, 2 and perpendicular to the planes x-y+2z=3 and 2x-2y+z+12=0, is :

Choose an option

Show full solutionCorrect option: C
Correct answer
C22

Step-by-step explanation

Let equation of plane be

ax-1+by-2+cz-2=0 .......i

Since (i) is perpendicular to the given planes, then

Dot product of the normal vectors of the perpendicular planes is 0.

a-b+2c=0

2a-2b+c=0

Solving above equations c=0 and a=b equation of plane i becomes x+y-3=0

Distance from 1, -2, 4 will be

D=1-2-31+1=42=22

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About this question

This is a previous-year question from JEE Main 2016, 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.