Three Dimensional Geometry Question 270
Question: If direction cosines of two lines are proportional to (2, 3, ?6) and (3, ?4, 5), then the acute angle between them is
[MP PET 2003]
Options:
A) $ {{\cos }^{-1}}( \frac{49}{36} ) $
B) $ {{\cos }^{-1}}( \frac{18\sqrt{2}}{35} ) $
C) $ 96{}^\circ $
D) $ {{\cos }^{-1}}( \frac{18}{35} ) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \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 =| \frac{(2),(3),+,(3),(-4),+(-6),(5)}{\sqrt{2^{2}+3^{2}+{{(-6)}^{2}}}.,\sqrt{3^{2}+{{(-4)}^{2}}+{{(5)}^{2}}}} | $ $ \cos \theta =\frac{18\sqrt{2}}{35} $
Þ $ \theta ={{\cos }^{-1}}( \frac{18\sqrt{2}}{35} ) $ .
BETA
