Three Dimensional Geometry Question 232
Question: The angle between the lines $ \frac{x+4}{1}=\frac{y-3}{2}=\frac{z+2}{3} $ and $ \frac{x}{3}=\frac{y-1}{-2}=\frac{z}{1} $ is
Options:
A) $ {{\sin }^{-1}}( \frac{1}{7} ) $
B) $ {{\cos }^{-1}}( \frac{2}{7} ) $
C) $ {{\cos }^{-1}}( \frac{1}{7} ) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Angle between two lines, $ \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}}} $
$ \therefore ,\cos \theta =\frac{1\times 3+2\times -2+3\times 1}{\sqrt{1^{2}+2^{2}+3^{2}}\sqrt{3^{2}+{{(-2)}^{2}}+1^{2}}} $ $ =\frac{2}{\sqrt{14}\sqrt{14}} $
$ \therefore \theta ={{\cos }^{-1}}( \frac{1}{7} ) $ .
BETA
