Three Dimensional Geometry Question 334
Question: The angle between the straight lines $ \frac{x-2}{2}=\frac{y-1}{5}=\frac{z+3}{-3} $ and $ \frac{x+1}{-1}=\frac{y-4}{8}=\frac{z-5}{4} $ is
[DCE 2005]
Options:
A) $ {{\cos }^{-1}}( \frac{13}{9\sqrt{38}} ) $
B) $ {{\cos }^{-1}}( \frac{26}{9\sqrt{38}} ) $
C) $ {{\cos }^{-1}}( \frac{4}{\sqrt{38}} ) $
D) $ {{\cos }^{-1}}( \frac{2\sqrt{2}}{\sqrt{19}} ) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \cos \theta =\frac{2\times (-1)+5\times 8+(-3)\times 4}{\sqrt{2^{2}+5^{2}+{{(-3)}^{2}}}\sqrt{{{(-1)}^{2}}+8^{2}+4^{2}}} $ $ \cos \theta =\frac{-2+40-12}{9\sqrt{38}} $ $ =( \frac{26}{9\sqrt{38}} ) $ \ $ \theta ={{\cos }^{-1}}( \frac{26}{9\sqrt{38}} ) $ .
BETA
