Coplanarity
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In geometry, a set of points in space is coplanar if the points all lie in the same geometric plane. For example, three points are always coplanar; but four points in space are usually not coplanar.
Points can be shown to be coplanar by determining that the scalar product of a vector that is normal to the plane and a vector from any point on the plane to the point being tested is 0.
Distance geometry provides a solution to the problem of determining if a set of points is coplanar, knowing only the distances between them.
[edit] Properties
If three 3-dimensional vectors 
and 
are coplanar, and 
, then
where 
denotes the unit vector in the direction of 
.
Or, the vector resolutes of on and on 
add to give the original .
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