JEE Main 2014MathematicsThree Dimensional GeometryMediumMCQ

JEE Main 2014 — Three Dimensional Geometry Question with Solution

JEE Main 2014 (09 Apr Online)

Question

A line in the 3-dimensional space makes an angle θ 0 < θ ≤ π 2 with both the X and Y-axes. Then, the set of all values of θ is in the interval :

Choose an option

Show full solutionCorrect option: C
Correct answer
C π 4 ,  π 2

Step-by-step explanation

cos 2 α + cos 2 β + cos 2 γ = 1

α = β = θ⇒ cos 2 γ + 2 cos 2 θ = 1

                     cos 2 γ = 1 - 2 cos 2 θ

0 ≤ cos 2 γ ≤ 1

0 ≤ 1 - 2 cos 2 θ ≤ 1

- 1 ≤ - 2 cos 2 θ ≤ 0

0 ≤ cos 2 θ ≤ 1 2    (as θ > 0 ,  cos θ < 1 )

⇒    0 ≤ cos θ ≤ 1 2

π 4 ≤ θ ≤ π 2

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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.