how can I do this in 3 space with for example points like this: for p1 = (3,0,3) p2 = (1,0,1) p3 = (1,2,3) I know N must be orthogonal to each point p2p1, p3p2, and p1p3.
The vectors defined by (p1, p2), (p1, p3) and (p2, p3) are all in the plane defined by p1, p2, and p3. Let us call these vectors A, B, and C. The cross-product of any two of A, B, and C will be normal to the plane.