Three Dimensional Geometry Question 9
Question: What is the angle between the lines $ \frac{x-2}{1}=\frac{y+1}{-2} $ and $ \frac{x-1}{1}=\frac{2y+3}{3}=\frac{z+5}{2}? $
Options:
A) $ \frac{\pi }{2} $
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{6} $
D) None of the above
Show Answer
Answer:
Correct Answer: A
Solution:
[a] The given lines are:- $ \frac{x-2}{1}=\frac{y-(-1)}{-2}=\frac{z-(-2)}{1} $ and $ \frac{x-1}{1}=\frac{y-( -\frac{3}{2} )}{\frac{3}{2}}=\frac{z-(-5)}{2} $ Dr?s of 1st line are:- $ a_1=1,b_1=-2,c_1=1 $ Dr?s of IInd line are:- $ a_2=2,b_2=3,c_2=4 $ Let $ ‘\theta ’ $ be the angle b/w two lines, then. $ \cos \theta =\frac{| a_1a_2+b_1b_2+c_1c_2 |}{\sqrt{a_1^{2}+b_1^{2}+c_1^{2}}.\sqrt{a_2^{2}+b_2^{2}+c_2^{2}}} $ $ \cos \theta =0 $
$ \Rightarrow \theta =\frac{\pi }{2} $
BETA
