Three Dimensional Geometry Question 218
Question: The angle between the lines whose direction cosines satisfy the equations $ l+m+n=0 $ , $ l^{2}+m^{2}-n^{2}=0 $ is given by
[MP PET 1993; RPET 2001]
Options:
A) $ \frac{2\pi }{3} $
B) $ \frac{\pi }{6} $
C) $ \frac{5\pi }{6} $
D) $ \frac{\pi }{3} $
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Answer:
Correct Answer: D
Solution:
$ l+m+n=0,l^{2}+m^{2}-n^{2}=0 $ and $ l^{2}+m^{2}+n^{2}=1 $ Solving above equations, we get $ m=\pm \frac{1}{\sqrt{2}},n=\pm \frac{1}{\sqrt{2}} $ and $ l=0 $ .
$ \therefore ,\theta =\frac{\pi }{3} $ or $ \frac{\pi }{2} $ .
BETA
