Three Dimensional Geometry Question 296
Question: The angle between two planes $ x+2y+2z=3 $ and $ -5x+3y+4z=9 $ is
[MP PET 2004]
Options:
A) $ {{\cos }^{-1}}\frac{3\sqrt{2}}{10} $
B) $ {{\cos }^{-1}}\frac{19\sqrt{2}}{30} $
C) $ {{\cos }^{-1}}\frac{9\sqrt{2}}{20} $
D) $ {{\cos }^{-1}}\frac{3\sqrt{2}}{5} $
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Answer:
Correct Answer: A
Solution:
Angle between two planes is, $ \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{(1),(-5),+(2),(3)+(2),(4)}{\sqrt{1^{2}+2^{2}+2^{2}}\sqrt{{{(-5)}^{2}}+3^{2}+4^{2}}} $ $ \cos \theta =\frac{3\sqrt{2}}{10}\Rightarrow \theta ={{\cos }^{-1}}( \frac{3\sqrt{2}}{10} ) $ .
BETA
