Three Dimensional Geometry Question 195
Question: The angle between the line $ \frac{x}{2}=\frac{y}{3}=\frac{z}{4} $ and the plane $ 3x+2y-3z=4 $ is
[MP PET 2003]
Options:
A) $ 45{}^\circ $
B) $ 0{}^\circ $
C) $ {{\cos }^{-1}}( \frac{24}{\sqrt{29}\sqrt{22}} ) $
D) $ 90{}^\circ $
Show Answer
Answer:
Correct Answer: B
Solution:
Angle between the plane and line is $ \sin \theta =\frac{a{a}’+b{b}’+c{c}’}{\sqrt{a^{2}+b^{2}+c^{2}}\sqrt{{{{{a}’}}^{2}}+{{{{b}’}}^{2}}+{{{{c}’}}^{2}}}} $ Here, $ a{a}’+b{b}’+c{c}’=2\times 3+3\times 2-4\times 3=0 $
$ \therefore \sin \theta =0 $
Þ $ \theta =0^{o}. $
BETA
