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

• be coincident,
• be parallel,
• have a point of intersection or
• be skew.

Instruction

For examining the positional relationship we use the following scheme.

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.