Consider 3 points P1,P2,P3 with coordinates x1,2,3 , y1,2,3 and z1,2,3 .............

consider the vectors P1P2 and P1P3 . then form the normal vector n = (P1P2 X P1P3)

to define the unique plane that passes through P1,P2,P3..... just get the scalar product between the normal vector and any vector P1P P(x,y,z) of the pane. You will obtain an equation ax+by+cz =d which is the equation of the plane you are looking for....