Can parallel lines be intersecting, and intersecting lines parallel?

By the definition of parallel lines in space, we have: two lines are called parallel if they do not intersect and lie in the same plane.

The definition of intersecting straight lines says: intersecting straight lines are non-intersecting straight lines that lie in different planes (they cannot quite, completely fall into one common plane).

Based on these definitions, we get: no, intersecting straight lines will never fall into one plane, so they will not become parallel. And vice versa.

And finally, these are two different types of arrangement of lines in space.