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A series of 3 points will always determine a plane unless 2 or all 3 points are identical points (they have the same coordinates).

If the idea is to have the three points determine oneplane, a unique plane, then three points will do that as long as none of them have the same spacial coordinates (have identical locations) or as long as the three points do not lie on a single line.

If a straight line can be drawn through all three points, they will not form one unique plane either.

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12y ago

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Q: When would three points not determine a plane?
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