Show that the conjecture below is false by finding a counterexample.

Question

Show that the conjecture below is false by finding a counterexample.

 If two lines do not intersect, then they are not coplanar lines.

Answer 1

As an example of what Mark stated in his answer, consider two parallel lines in the x-y plane:

 

y = mx + b₁

y = mx + b₂

 

They are coplanar, but they do not intersect if b₁ ≠ b₂.  So you have 2 lines that do not intersect, yet are coplanar.

Answer 2

Two parallel lines do not intersect and they can be coplanar.