I'm reading a book on information retrieval and in it there is an example where they have two sets of vectors.
They compute the centroid vectors for both the sets and then give the equation of a plane that divides the space into two parts equidistant from the centroid vectors between them.
I would like to know what is the method to get the equation of such a plane.
I know that given two points on a plane if you would like to find an analogous line that does the same with the points, you would connect the two points, draw a normal at the midpoint of the line connecting the points, and this normal would do the same thing that the plane does in my example. However since I have a bad background in mathematics, I can't write this mathematically, and I can't precisely think how this would work in my case.
Thank you for your time.
Edit: The two centroid vectors in my example are: 0a+0b+0c+0.33d+0.33e+0.33f and 0a+0.71b+0.71c+0d+0e+0f
and the equation of the hyperplane that divides them is:
[0 -0.71 -0.71 0.33 0.33 0.33]x= -1/3
We can get the matrix on the LHS by subtracting the two given vectors, but how does this work? And I also do not know how do we get the constant on the right?
I apologize for the bad formatting, I do not know how to use TeX