# 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.

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### Remember

Lines that are neither intersecting nor parallel are referred to as

**skew**.## Instruction

For examining the positional relationship we use the following scheme.

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

#### 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**.#### 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**.