Question

can a pair of lines be both parallel and skew? Explain.

Answer 1

okay, so this is the mathematical definition of skew:
2 Mathematics (of a pair of lines) neither parallel nor intersecting.
• (of a curve) not lying in a plane.

Answer 2

no. because, if they are parallel, then they are in the same plane. If they are skew, then they are not in the same plane.

Answer 3

so they cannot be BOTH parallel AND skew because the definition of skew states that they cannot be parallel so if it's parallel, it is not skew and if it is skew, then it is not parallel. So they cannot BOTH Be parallel and skew :)