Weighted geometric median (Weber problem)

Topic:
Vectors
This activity belongs to the GeoGebra book Attractive projects. 3D project: create automatic dynamic demonstrations. If we associate a weight with each vertex, the weighted geometric median will be the point that minimizes the sum of the "moments" (weight products per distance) to the vertices. Physically, it corresponds to the equilibrium point of a ring from which strings to each vertex with hunging weights at their ends. (Note that if the weight of one vertex is k times that of another, the ratio between the volumes of the spherical weights will be k, and therefore the ratio between their radii will be the cubic root of k.)