Infinitely long prism is sliced

[vectorspaces]

Homework Statement

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?

Homework Equations

I don't know...no idea really

The Attempt at a Solution

I think it would be a parallelogram, but I have no idea how to prove this.

 

[Spinnor]

What class is this for?

 

[Spinnor]

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.