Math Relative position of lines Positional relationship of two lines

Positional relationship of two lines

The positional relationship of two lines provides information on how two lines within a coordinate system are positioned to one another.

A distinction is made between four possible positional relationships for lines in three-dimensional space. The lines can



Lines that are neither intersecting nor parallel are referred to as skew.


For examining the positional relationship we use the following scheme.

Positional relationship

First, check if the direction vectors of the lines are collinear.

  1. The direction vectors are collinear:

    That means the lines are parallel. If they have a random point (e. g. position vector) in common they are coincident. Otherwise they are parallel.
  2. The direction vectors are not collinear:

    In this case the direction vectors are equated. The solution of the equation corresponds to the point of intersection (lines intersect). If there is no definite solution the lines are skew.