True or false

this would be true.

By definition a plane is a flat surface that has no thickness and extends forever, if we take a cube we know that the top and the bottom of the cube are parallel to each other, so if in 3D space we have a cube that is 2x2x2.

The bottom of the cube would we lying in a plane that is defined by z = 0, and its top is lying in the plane where z = 2. We know that the top and bottom of the cube are parallel to each other, so the planes that contain the top and the bottom are also parallel to each other. They will not intersect

## Comments

Michelle raised a good point. You can write the equations of two planes in the Hessian normal form, i.e., for example

2x+3y-1=0

2x+3y-2=0

The two equations defined two planes in R3, and you can easily verify that they have no point in common. Hence, in Euclidean geometry, they must be parallel.