JEE Mains · Maths · STD 12 - 11. three dimension geometry
Each of the angles \(\beta\) and \(\gamma\) that a given line makes with the positive y - and z -axes, respectively, is half of the angle that this line makes with the positive x -axes. Then the sum of all possible values of the angle \(\beta\) is
- A \(\frac{3 \pi}{4}\)
- B \(\pi\)
- C \(\frac{\pi}{2}\)
- D \(\frac{3 \pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{3 \pi}{4}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \beta=\frac{\alpha}{2}, \gamma=\frac{\alpha}{2} \\ & \cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1 \\ & \cos ^2 \alpha+2 \cos ^2 \frac{\alpha}{2}=1 \\ & \cos ^2 \alpha+\cos \alpha=0 \\ & \cos \alpha(\cos \alpha+1)=0 \\ & \cos \alpha=0,-1 \\ &…
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