Coplanar and Non-coplanar Vectors
Concept
Definition: Any finite number of vectors are called coplanar vectors if they lie on the same plane or parallel planes.
If the vectors are coplanar them we can always draw a parallel plane to all of them. Similarly, a finite number of vectors are said to be non-coplanar if they do not lie on the same plane or on the parallel planes. In this case we cannot draw a single plane parallel to all of them.
Theorem: If and be any three non-zero and non-coplanar space vectors such that then x = y = z = 0