Three Dimensional Geometry Question 46
Question: What is the equation of the plane through z-axis and parallel to the line $ \frac{x-1}{\cos \theta }=\frac{y+2}{\sin \theta }=\frac{z-3}{0} $ ?
Options:
A) $ xcot,\theta +y=0 $
B) $ xtan\theta -y=0 $
C) $ x+ycot,\theta =0 $
D) $ x-ytan,\theta =0 $
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Answer:
Correct Answer: B
Solution:
[b] Let equation of plane through z-axis is $ ax+by=0 $ It is given that this plane is parallel to the line $ \frac{x-1}{\cos \theta }=\frac{y+2}{\sin \theta }=\frac{z-3}{0} $ Since the plane parallel to the line
$ \therefore a\cos \theta +b\sin \theta =0 $
$ \Rightarrow a\cos \theta =-b\sin \theta \Rightarrow a=-b\tan \theta $
$ \therefore -b\tan \theta x+by=0 $
$ \Rightarrow x\tan \theta -y=0(\therefore b\ne 0) $ Which is required equation of plane.
BETA
