JEE Main 2014MathematicsThree Dimensional GeometryEasyMCQ

JEE Main 2014 — Three Dimensional Geometry Question with Solution

JEE Main 2014 (06 Apr)

Question

The angle between the lines whose direction cosines satisfy the equations l⁡+m+n=0 and l⁡2=m2+n2 is 

Choose an option

Show full solutionCorrect option: C
Correct answer
C π 3

Step-by-step explanation

l⁡+m+n=0

m+n=-l⁡

∴   m+n2=l⁡2

∴   l⁡2= m2+n2+2mn

But, m2+n2=l⁡2

∴   2mn=0

∴  m = 0 or n = 0

∴  l⁡=-n or l⁡=-m

∵l⁡2+m2+n2=1

∴  The two direction cosines are 12,0,-12 and 12,-12,0

θ  is the angle between them.

∴   cos θ=l1l2+m1m2+n1n2=1212+0+0=12

∴    θ = π 3 .

Note : Taking l⁡ = - 1 2 , will also given the same solution, but the supplementary angle. Both are correct, we choose the one present in the options.

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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.