> 1) I stated that it is a 3 by n array, hence 3n dots. >
Well, for those who work with homogeneous coordinates, 3 coordinates for a single point is not really surprising. And as those people, including me, usually write down n points as an 3 by n matrix, it's better to ask, isn't it?
> 2) I stated that they are "in one plane" so there is no 3-space to > consider.
Again, there is no problem with having a plane in 3-space. And if you think projectively, 3-space isn't that far from the projective plane.
Now, let me ask another question, because I still don't understand your question: What are the entries of the 3 by n matrix? What exactly do you mean by "dot"?