A straight line satisfies the following condition.
- $p>0$ is the length of the perpendicular on the line from the origin
- $\alpha$ is the angle made by this perpendicular with the positive $x$-axis.
Vectorically derive that the equation of this straight line is $$x \cos\alpha + y \sin\alpha =p$$
With some ideas I have made a figure. But not sure that the figure is correct. Please help me with this and the further derivation.