Geometric objects lying in a common plane are said to be coplanar. Three noncollinear points determine a plane and so are trivially coplanar. Four points are coplanar iff the volume of the tetrahedron defined by them is 0,
 |
Coplanarity is equivalent to the statement that the pair of lines determined by the four points are not skew, and can be equivalently stated in vector form as
![(x_3-x_1)·[(x_2-x_1)x(x_4-x_3)]=0.](/images/equations/Coplanar/NumberedEquation2.svg) |
An arbitrary number of 
points 
, ..., 
can be tested for coplanarity by finding the point-plane
distances of the points 
,
..., 
from the plane
determined by 
and checking if they are all zero. If so, the points are all coplanar.
A set of 
vectors 
is coplanar if the nullity
of the linear mapping defined by 
has dimension 1, the matrix rank
of 
(or equivalently, the number of its
singular values) is 
(Abbott 2004).
Parallel lines in three-dimensional space are coplanar, but skew lines are not.
