Question

What are skew lines? Do they lie in the same plane?

Answer 1

Please see below.

Explanation:

In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel.

It is obvious that if two lines lie in the same plane, they must either intersect each other or are parallel.

Therefore, skew lines can exist only in three or more dimensions and two lines are skew, if and only if, they are not in the same plane. For example see in the figure below.

Observe that line `AB` lies in the shown plane and although line `CD` intersects the plane, the point of intersection of line with the plane does not lie on line `AB`. Hence, `AB` and `CD` are skew lines.