a line perpendicular to a given line

Question

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

Answer 1

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.