A set of points is set to be coplanar if and only if they lie on the same geometric plane. Three points are always coplanar.
Other points can be shown to be coplanar by determining that the scalar product of a vector normal to the plane and a vector from any point on the plane to the point being tested is 0.
Properties
If three 3-dimensional vectors 
and 
are coplanar, and 
:
Or, the vector resolutes of on 
and on 
add to give the original .
External links
MathWorld's entry on "coplanar"