Planes Question

Question

Give the equations of three planes that meet in three lines. Explain your reasoning? It creates a triangular prism..

Can anyone help me with this? I found the equations but do not know how to explain them.

The three equations are:

$4x + y - 2z = 0 $

$2x - y - 4z = 0 $

$ x + y + z = 6 $

Answer 1

I'd consider taking a look at this.

You want to show that all 3 planes are NOT parallel by considering the plane's normals. Also consider the intersections: The lines that the planes meet at should have the same slopes i.e. be parallel for a triangular prism.

Answer 2

Here are three planes in the $x-y-z$ coordinates satisfying the desired conditions:

$$x=0, ~y=0, ~y+x=7$$