Problem about planes Say we have $2x+3y+3z=0$ which is a plane.
Does that plane have infinite dimensions (it is a 2D "object" — forgive me as I am not a mathematician — but each side has infinite length) or is it just the parallelogram that is defined by the vectors $[2,3,3]$ and $[x,y,z]$?
I think its the first one because the solution to that equation is all the vectors that are perpendicular to $[2,3,3]$ which are infinite.

There are many different types of/ definitions of dimensions in Mathematics. As a vector space, the plane (since it goes through the origin) is 2-dimensional, in the sense that every vector in the plane can be written as the linear combination of two vectors. In another sense, the dimension is 2, in that, if you know the value of any two of the coordinates of a point in the plane, you can uniquely locate the point in the plane. Sorry, but this is an intrinsically-technical issue and I cant see how to avoid bring up the different definitions.
