Well, it depends on whether you're talking about a coordinate plane, or a flying plane. You can graph points on a coordinate plane, that's easy. But the flying kind of plane, there are lots of angles involved; at what angle do I take-off/land? Speed, that's another thing, you need speed to be able to stay in the air. That requires math.
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Two lines that lie on different planes but are not parallel.
Edges are one dimensional objects where two planes meet.
A riddle, by its nature, is usually a question in disguise. So if it is given to you as a mathematical question, it is very likely that the answer has nothing to do with mathematics.
it can fly
An element is anything that is put into a set. In math, this can be just about anything you can talk about in math: for example, different types of numbers; points; polygons; lines; planes; matrices; operations; functions; sets; and many other more.