Three Dimensional Geometry Question 249
Question: The angle between a line with direction ratios 2 : 2 : 1 and a line joining (3, 1, 4) to (7, 2, 12) is
[DCE 2002]
Options:
A) $ {{\cos }^{-1}}(2/3) $
B) $ {{\cos }^{-1}}(-2/3) $
C) $ {{\tan }^{-1}}(2/3) $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
D.r?s are 2, 2, 1 and $ (7-3,2-1,12-4)\equiv (4,,1,,8) $ \ $ \cos \theta =\frac{2\times 4+2\times 1+1\times 8}{\sqrt{2^{2}+2^{2}+1^{2}}\sqrt{4^{2}+1^{2}+8^{2}}}=\frac{18}{9\times 3}=\frac{2}{3} $ Hence, $ \theta ={{\cos }^{-1}}(2/3) $ .
BETA
