Points, vectors, matrices

I'm having real trouble making this correlation. I know what points and vectors are in definition. What I don't understand is, from what I can tell, you write a point as x,y,z and you write a vector as x, y, z. This is puzzling, since vectors have a magnitude and direction. How can I tell that from x,y,z?

Right along with this is the difference between vectors and real values. Are real values points? I know dot products give you real values, and cross products give you another vector.

Next is vectors to matrices. How a vector becomes a 3x3 matrix or what is contained in a 3x3 matrix is beyond me. And yes, I have books. They detail formulas out very nicely. But the holes in their explanations are described above. I mainly see sections on points, vectors, and matrices. But not how they go together or even if they do.

This may be a lot of questions for one post, but then again, they may all get answered in one sentence. I don't know. If you know the answer to any or all, please point me in the right direction.

subnet_rx

"There are two types of langages, those that everyone *****es about, and those that no one uses."