In three-dimensional Euclidean space, parallel lines not only fail to intersect, but also maintain
a constant separation between points closest to each other on the two lines. Therefore,
parallel lines in three-space lie in a single plane (Kern
and Blank 1948, p. 9). Lines in three-space which are not parallel but do not
intersect are called skew
lines.
Kern, W. F. and Bland, J. R. Solid Mensuration with Proofs, 2nd ed. New York: Wiley, p. 9, 1948.Kimberling,
C. "Triangle Centers and Central Triangles." Congr. Numer.129,
1-295, 1998.