JEE Main 2017MathematicsThree Dimensional GeometryMediumMCQ

JEE Main 2017 — Three Dimensional Geometry Question with Solution

JEE Main 2017 (02 Apr)

Question

The distance of the point 1, 3,-7 from the plane passing through the point 1,-1,-1 , having normal perpendicular to both the lines x-11=y+2-2=z-43 and x-22=y+1-1=z+7-1 , is:

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Show full solutionCorrect option: B
Correct answer
B1083

Step-by-step explanation

Let l, m, n be the direction cosines of the line normal to the plane, then

l-2m+3n=0 and 2l-m-n=0

⇒l2+3=m6+1=n-1+4=λ

⇒l=5λ, m=7λ, n=3λ

∴ The equation of the plane is

5x+7y+3y+d=0

∵ it passes through 1,-1,-1

⇒5-7-3+d=0

⇒d=5

Hence, the equation of the plane is 5x+7y+3y+5=0

Now, PQ=5+21-21+552+72+32

⇒PQ=1025+49+9

⇒PQ=1083

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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.