Three Dimensional Geometry Question 227
Question: The angle between the lines whose direction cosines are connected by the relations $ l+m+n=0 $ and $ 2lm+2nl-mn=0 $ , is
Options:
A) $ \frac{\pi }{3} $
B) $ \frac{2\pi }{3} $
C) $ \pi $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Eliminating n, we have $ (2l+m),(l-m)=0 $ When $ 2l+m=0, $ then $ \frac{l}{1}=\frac{m}{-2}=\frac{n}{1} $ When $ l-m=0, $ then $ \frac{l}{1}=\frac{m}{1}=\frac{n}{-2} $
$ \therefore $ Direction ratios are 1, ? 2, 1 and 1, 1, ? 2. $ \cos \theta =\frac{\sum a_1a_2}{\sqrt{(\sum a_1^{2}),}.\sqrt{(\sum a_2^{2}),}}=-\frac{1}{2}, $
$ \Rightarrow \theta =120^{o}=\frac{2\pi }{3}. $
BETA
