I was reading this blog about how to compute intersections in the real projective plane and I'm struggling with this sentence:
Notice that the POINT (a, b, c) is contained in the LINE [x, y, z] exactly if ax + by + cz = 0
Can you explain this a bit Better by example, please?
Thanks in advance
EDIT: I'll try to explain Better my concern. Usually a point defines a line in 3d Euclidean space. Here that line will be perpendicular to the Plane ax + by + cz = 0, which the 3d representation of the [a, b, c] line. So I can't see how the point can lie on that plane, since being part of a 3dline perpendicular to It (modulo being the origin)