Write down a necessary and sufficient condition on any three points in R3 such that the three points lie on a plane that corresponds to a subspace of R3. Justify your answer.

Hint:Prove that any three vectors are coplanar,if and only ifthey are linearly dependent. You also need to prove that the span made from any three linearly dependent vectors(including zero vector)will be a subspace of R3.

Note:Please do not usedim() or determinant or dot product. Use linear dependent, subspace, span, bases concept only!