As opposed to 3 colinear points, 3 non-collinear points are used to define a plane because they constitute linearly independent vectors.
Why are specific planes identified using 3 non-collinear points vs. 3 collinear points?
The reason why 3 non-collinear points are used to define a plane is because the dimension of a plane is 2, hence, it follows that exactly two linearly independent vectors are needed to constitute a plane.
It consequently follows that two independent vectors can be formed by the 3 non-collinear points where one point serves as the origin and the other two are the tips of the vectors.
Read more on colinear points;
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