Why are specific planes identified using 3 non-collinear points vs. 3 collinear points?

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22-08-2022
Mathematics

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Why are specific planes identified using 3 non-collinear points vs. 3 collinear points?

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adioabiola adioabiola · Answer 1 · 2022-08-23T16:28:39+02:00

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.