Two lines are coplanar if they lie in the same plane or in parallel planes. There is ALWAYS a plane which contains two parallel lines (see first attached image for details).
Two lines that lie in parallel planes are sometimes parallel. For example, see at second image. Planes and are parallel. Consider pair of lines and - they are parallel, but if you consider the pair of lines and , you can see they are not parallel.
By definition parallel lines are lines in a plane which do not meet, that means, they have to be coplanar. Coplanar means they are included in the same plane. Then, two parallel lines are always coplanar (imagine two parallel lines in a 3d space, there is always a plane that can contain them).
Two lines that lie in parallel planes are sometimes parallel. As stated before, if there is a third plane which contains the two lines, they can be parallel or cannot, but if there is no plane which contains them, they are not parallel.
Thus, 2/3 is the simplified fraction for 18/27 by using the GCD or HCF method. Thus, 2/3 is the simplified fraction for 18/27 by using the prime factorization method
