The point is on both spheres.
so if two spheres intersect (one with centre (1,1,2) and radius R=4 and the other with centre (1,1,4) with radius r=2) (i just made these values up i hope they work). how can you find the PLANE that is defined by the intersection of both spheres (actually it's a circle but let's call it a plane)
The normal vector of the plane is obvious, it must be the vecto C1C2 (the vector between centre 1 and centre 2)
but how do you find the known point on the sphere then?
HELP very appreciated! thanks!
The first sphere has the equation:
The 2nd sphere has the equation:
Subtract both equations. You'll get:
which is the equation of the plane which contains the common points of both spheres. With your example the equation describes the tangent plane of both spheres.