So there's something in my linear algebra textbook that I just can't understand.
Here goes: (keep in mind that the textbook is not in English so my translation may not be the best):
The line l can be determined by a point P that's on that line and a vector n that's orthogonal to the line. Let's pick the point O as the center of a coordinate system. Then, the point X is on the line l if and only if PX is orthogonal to n, meaning:
$PX \cdot n = 0$
Using the position vectors of the points P and X we get:
$r \cdot n = p$
where p is a constant and $r = OX$
And here's the illustration that follows (redrawn by me, but it's exactly like in the textbook):
Things I don't get here:
What the hell is p (the small one)? How is this even an equation of a line?
There is also a part about parametric representation of the line which, oddly, comes before this part in the textbook, and that one I understood. But this I just can't get through my head, it seems as if there is a lack of information or something. Anyhow I've googled this a lot and couldn't find anything like it. In the textbook this is called 'vector equation of a line' whereas when I google that I get the parametric equation of a line which is a different thing I suppose. I would gladly skip this but the problem is that it is used as a step in a proof for the distance between a point and a line. So if anyone could explain me what's going on here, that would be nice.
Thanks in advance.