JEE Main 2018MathematicsThree Dimensional GeometryHardMCQ

JEE Main 2018Three Dimensional Geometry Question with Solution

JEE Main 2018 (08 Apr)

Question

If L1 is the line of intersection of the planes 2x-2y+3z-2=0, x-y+z+1=0 and L2 is the line of intersection of the planes x+2y-z-3=0, 3x-y+2z-1=0, then the distance of the origin from the plane, containing the lines L1 and L2 is

Choose an option

Show full solutionCorrect option: C
Correct answer
C132

Step-by-step explanation

Direction Ratio's of the line L1

ijk2-231-11

=i1-j -1+k(0)

= 1, 1, 0

At y=0

2x+3z=2x+z=-1  (-5,0,4) is point

Equation of L1

x+51=y1=z-40=α

Similarly for L2

x-753=y-5=z+85-7=β

Point of intersection of L1 and L2

(-1,4,4)

Direction Ratio's of normal to plane passing through L1 and L2 =ijk1103-5-7=i-7-j-7+k-5-3=-7i+7j-8k=-7, 7, -8

Equation of plane

-7x+7y-8z=c .

c=3   (Since plane passes through(-1,4,4) )

Equation of plane

7x-7y+8 z+3=0

Distance from origin

=372+-72+82=3162=392

=132
 

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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.