# a line perpendicular to a given line

I am confused now,

I have a 2D line. If its equation is $r = x\cos(\theta) + y\sin(\theta)$, then what will be the line which is perpendicular to that line?

Where $r, \theta$ is described here.

I know this is very simple, any suggestions please. thanks

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A line perpendicular to your line is

$$-x \sin{\theta} + y \cos{\theta} = C$$

That said, looking at your reference, that equation is the equation of a line perpendicular to a radius vector from the origin at angle $\theta$ with respect to the positive $x$ axis, at a distance $r$ from the origin.

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thank you very much. what is the general rule to get it, please. wish to learn – niro Feb 17 '13 at 11:31
Then general rule is a line perpendicular to $a x + b y = c_1$ is $-b x + a y = c_2$. – Ron Gordon Feb 17 '13 at 11:34
sorry for making confuse. i would like to know how it decide.. does make a vector? if so it wil be rotated vector, then how it would be... – niro Feb 17 '13 at 11:35