Coplanar vectors:
- The 3 vectors
are coplanar if there exists l, mÎR such that 
that is one can be expressed as a linear combination of the other 2.
- If
are coplanar (essential and sufficient condition).
- The 4 points
lie in the same plane if there exist l, m∈R such that 
- If
are coplanar.
- A, B, C, D are coplanar if there exists scalars k, l, m, n, such that
where k + l + m + n = o.
Again all above methods are equivalent. Choose the best amongst them depending on convenience.
Illustration: Prove that if 
, then the vectors 
can never be coplanar.
Key concept: If the 3 vectors
are coplanar then 
.
Solution: Assume that are coplanar.
Therefore they cannot be coplanar
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