A) \[\pi /6\]
B) \[\pi /4\]
C) \[\pi /2\]
D) \[\pi /3\]
Correct Answer: B
Solution :
[b] Consider a line |
\[x\,\,\cos \theta +y\,\sin \theta =2\] |
\[\Rightarrow y\sin \theta =-x\cos \theta +2\] |
\[\Rightarrow y=-x\frac{\cos \theta }{\sin \theta }+\frac{2}{\sin \theta }\] |
\[\Rightarrow y=-x\cot \theta +2\cos ec\theta \] |
On comparing this equation with |
\[y=mx+c\] we get |
slope of line \[x\,\,\cos \theta +y\,\,\sin \theta =2\,\,is\,\,-\cot \,\,\theta \] |
Also, we have a line \[x-y=3\] is 1. |
\[\Rightarrow \,\,\,\,\,\,\,\,\,y=x-3\] |
slope of line \[x-y=3\] is 1. |
Since, both the lines are perpendicular to each other |
\[\therefore \] Product of their slopes = -1 |
\[\Rightarrow (-cot\theta )(1)=-1\] |
\[\Rightarrow cot\theta =1=\cot \frac{\pi }{4}\] |
\[\Rightarrow \theta =\frac{\pi }{4}\] |
You need to login to perform this action.
You will be redirected in
3 sec