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.

If you are asking if the plane is unbounded, indeed it is. Equivalently in this case the area of the plane thus described is infinite.
