Question

are 2 non-coplanar lines always skew? explain

Answer 1

Two lines are said to be skew lines if they do not intersect each other and are also not parallel to each other.

Now, if the two lines are parallel, they will lie on the same plane.
and if the two lines intersect each other at a point, then also they will lie on same plane passing through that point.
In both the above cases, the lines will be coplanar, since they will lie on the same plane.

Thus, the two lines, if neither intersecting each other nor are parallel will not be coplanar. In other words, they will always be non-coplanar.And this implies that the skew lines are are always non-coplanar.