Do two planes always intersect in exactly one line?

Question

Could you show that this conjecture is false by one counter example.

Please explain!

Answer 1

They can be skew and not intersect at all.

Answer 2

They can be parallel.

So, no do not always intersect.

Imagine the plane of the extension of the floor of your house.

Imagine the plane of the extension of a flat roof on the house.

They never intersect.

:)

Answer 3

The plane z=0 and the plane z=1 do not intersect because 0 does not equal 1.