JEE Main 2014MathematicsThree Dimensional GeometryEasyMCQ

JEE Main 2014 — Three Dimensional Geometry Question with Solution

JEE Main 2014 (19 Apr Online)

Question

If the angle between the line 2x⁡+1=y⁡=z⁡+4 and the plane 2x⁡-y⁡+λz⁡+4=0 is π 6 , then the value of λ  is

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Show full solutionCorrect option: A
Correct answer
A 4 5 7

Step-by-step explanation

Given line is L:x+11=y2=z+42 and plane is P: 2x-y+λz+4=0.

The angle between a line x-x1l=y-y1m=z-z1n and a plane ax+by+cz+d=0 is 

sinθ=al+bm+cna2+b2+c2l2+m2+n2

         

sinπ6=2×1+-1×2+2λ12+22+2222+12+λ

⇒12=2-2+2λ1+4+44+1+λ

⇒12=2λ35+λ

⇒4λ=35+λ

Squaring both sides, we get

⇒16λ=95+λ

⇒16λ=45+9λ

⇒7λ=45

⇒λ=457.

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About this question

This is a previous-year question from JEE Main 2014, 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.