A) \[x\,\,cot\,\theta +y=0\]
B) \[x\,\,tan\,\,\theta -y=0\]
C) \[x+y\,\,cot\,\theta =0\]
D) \[x-y\,\,tan\,\theta =0\]
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.
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