In geometry, skew lines are a pair of lines that do not intersect and are not parallel to each other. Skew lines can only exist in dimensions higher than 2D space, and they have to be non-coplanar, meaning that such lines exist in different planes. In two-dimensional space, two lines can either be intersecting or parallel to each other, so skew lines can never exist in 2D space. Skew lines can be found in many real-life situations. For example, if there is a line on a wall and a line on the ceiling, and these lines are not parallel to each other and do not intersect, then they can be skew lines as they lie in different planes.

In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. Two lines that both lie in the same plane must either cross each other or be parallel, so skew lines can exist only in three or more dimensions. Two lines are skew if and only if they are not coplanar. Testing for skewness, if each line in a pair of skew lines is defined by two points that it passes through, then these four points must not be coplanar, so they must be the vertices of a tetrahedron of nonzero volume. 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 summary, skew lines are lines that do not intersect and are not parallel to each other, and they can only exist in dimensions higher than 2D space.