Question

Is it possible to draw three lines in two planes such that all three lines are skew?

Answer 1

Yes; it is possible 

If the planes are parallel to each other then they don't intersect. 

There can also be two or more lines on different planes which do not intersect each other. These lines are called skew lines.

Answer 2

Answer with explanation:

→Two lines in three dimensional plane are said to be Skew if they are neither parallel nor Intersecting.

→Skew lines can be drawn in three dimensional plane only.

→Drawn two skew lines in a Plane , and then drawn another line in a plane and found that , they are skew.

⇒Yes, it is possible to draw three lines in two planes such that all three lines are skew.