Two or more lines which have no intersections but are not parallel, also called agonic lines. Since two lines in the plane must intersect or be parallel, skew lines can exist only in three or more dimensions.
Two lines with equations
(1)
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(2)
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are skew if
(3)
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(Gellert et al. 1989, p. 539).
This is equivalent to the statement that the vertices of the lines are not coplanar, i.e.,
(4)
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Three skew lines always define a one-sheeted hyperboloid, except in the case where they are all parallel to a single plane but not to each other. In this case, they determine a hyperbolic paraboloid (Hilbert and Cohn-Vossen 1999, p. 15).