Three Dimensional Geometry Question 6
Question: The plane $ 2x-3y+6z-11=0 $ makes an angle $ {{\sin }^{-1}}(a) $ with the x-axis. Then the value of a is-
Options:
A) $ \frac{\sqrt{3}}{2} $
B) $ \frac{\sqrt{2}}{3} $
C) $ \frac{3}{7} $
D) $ \frac{2}{7} $
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Answer:
Correct Answer: D
Solution:
[d]
$ \therefore $ DR?s of the normal of the plane $ =2,-3,6 $ and Dr?s of x-axis is 1, 0, 0 And if $ \theta $ is the angle between the plane and x-axis, then $ \sin \theta $ $ =\frac{2(1)+(-3)(0)+(6)(0)}{\sqrt{2^{2}+{{(-3)}^{2}}+6^{2}}\sqrt{1}}=\frac{2}{7} $
$ \Rightarrow \theta ={{\sin }^{-1}}( \frac{2}{7} )\therefore a=\frac{2}{7} $
BETA
