Equations:

Symmetric form for describing the straight line:

1.  Line through  parallel to the vector (a, b, c):

2. Line through point and :

This line is parallel to the vector

Parametric Form

In three-dimensional space, the line passing through the point and parallel to (a, b, c) has parametric equations

In three-dimensional space, the line passing through the point and

Intersection:

The line through  in direction and the line through in direction  intersect iff:

Parallelism:

Three lines with directions are parallel to a common plane if and only if

Distance:

Distance between the point  and the line through  in direction (a, b, c):

Distance between the line through  in direction and the line through in direction :