JEE Mains · Maths · STD 12 - 11. three dimension geometry
A line in the \(3-\) dimensional space makes an angle \(\theta \left( {0 < \theta \le \frac{\pi }{2}} \right)\) with both the \(x\) and \(y\) axes. Then the set ofall values of \(\theta \) is the interval
- A \(\left( {0,\frac{\pi }{4}} \right]\)
- B \(\left[ {\frac{\pi }{6},\frac{\pi }{3}} \right]\)
- C \(\left[ {\frac{\pi }{4},\frac{\pi }{2}} \right]\)
- D \(\left( {\frac{\pi }{3},\frac{\pi }{2}} \right]\)
Answer & Solution
Correct Answer
(C) \(\left[ {\frac{\pi }{4},\frac{\pi }{2}} \right]\)
Step-by-step Solution
Detailed explanation
It makes \(\theta\) with \(x\) and \(y\) -axes. \(l=\cos \theta, m=\cos \theta, n=\cos (\pi-2 \theta)\) we have \(l^{2}+m^{2}+n^{2}=1\) \(\Rightarrow \cos ^{2} \theta+\cos ^{2} \theta+\cos ^{2}(\pi-2 \theta)=1\) \(\Rightarrow 2 \cos ^{2} \theta+(-\cos 2 \theta)^{2}=1\)…
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