The way it seems to me, linearly dependent vectors have to be collinear, and collinear vectors have to be coplanar. However, since a plane doesn't really have a direction, I'm assuming coplanar vectors can point in different directions as long as their lines exist on the same plane. Or do coplanar vectors/points also have to point in the same direction? If so, what's the practical difference between these concepts? I'm wondering this in terms of orientation and position in three-space, not in terms of whether the math is done differently or not.
For example, what would be the difference between 3 linearly dependent vectors, 3 collinear vectors and 3 coplanar vectors?
EDIT: So far I still can't visualize the difference in 3D space. It's not that I don't understand that the math is different, I just want to be able to clearly visualize what the similarities and differences are, because if I don't then the math won't make sense to me. I need to understand what the math does in order to make it stick.