Question

is 4x-2y+4z=5 parallel to 4x-2y+4z=-11 ?

Answer 1

Yes of course they are. The coefficients of the coordinates are same, only the constant is varying.

Answer 2

I thought so but was not sure. I cannot visualise 3D graphs well :(

Answer 3

Aw just give it a try. Here's what I do- Just look at the corner of the room, could be the floor or the roof. The point where 3 faces of the room are meeting. Now you can visualise a cube/cuboid easily. :)

Answer 4

If I remember right, the norms of parallel planes are scalar multiple: the norm is exactly the same <4,-2,4>