Multiple Planes

The relationships between lines and planes are a bit complicated. As we mentioned, any single line can be contained in a plane. Sometimes, though, you have two lines that cannot be contained in a single plane.

AB and DE cannot be contained in a single plane. In this situation, we say the lines are skew. Skew lines are kind of weird—they don't intersect each other, but they're not quite parallel either. If parallel lines were friends and intersecting lines were enemies, skew lines would be people who have never met and don't care about each other one bit.

What about planes interacting with other planes? In three-dimensional space, planes are either parallel or intersecting (in higher dimensional spaces you can have skew planes, but that's too trippy to think about). Parallel planes never meet, looking kind of like this:

Intersecting planes intersect each other. Shocker. They look a little something like this:

Well, as we can see from the picture, the planes intersect in several points. In fact, they intersect in a whole line! If you imagine two intersecting planes as the monitor and keyboard of a laptop, their intersection is the line containing those flimsy joints that you're always paranoid airport security will break when inspecting your computer.

Three planes can intersect at a point, but if we move beyond 3D geometry, they'll do all sorts of funny things. Fortunately, we won't go past 3D geometry. We just thought we should warn you in case you ever find yourself in an alternate universe or the seventh dimension thinking, "I wonder if planes here work the same way."