JEE Main 2010 — Three Dimensional Geometry Question with Solution
JEE Main 2010
Question
A line in three-dimensional space makes angles and with the positive -axis and the positive -axis respectively. If makes an acute angle with the positive -axis, then equals
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
where is the angle which line makes with positive z-axis.
Now
\begin{aligned}
& \Rightarrow \frac{1}{2}+\frac{1}{4}+\cos ^2 \theta=1 \\
& \cos ^2 \theta=\frac{1}{4} \\
& \Rightarrow \cos \theta=\frac{1}{2} ( $\theta$ Being acute)\\
& \Rightarrow \theta=\frac{\pi}{3}
\end{aligned}
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This is a previous-year question from JEE Main 2010, 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.