1. The problem statement, all variables and given/known data What happens when an infinitely tall vertical rectangular prism consisting of all (x,y,z) with x between a and b and y between c and d is cut by a non-vertical plane z = px + qy + k? What are the possible shapes of the slice? 2. Relevant equations I don't know...no idea really 3. The attempt at a solution I think it would be a parallelogram, but I have no idea how to prove this.
Imagine viewing a rectangular piece of paper at some distance. All possible orientations of the paper except those you when you view the paper head on will give you the possible shapes you are looking for? It might help to pick up a playing card, drivers license, or credit card and hold it at arms length.