Problem. Let A(-1,3,-2), B(-3,7,-18), C(2,-1,-3) be three points and (P):
2*x - y +z + 1 = 0 be a plane. Find the coordinates of the point M lies on the plane (P) so that MA^2 + 2MB^2 + 3MC^2 obtain the minimum value.
This is my code.
restart: with(geom3d):
A:=<-1,3,2>: B:=<-3, 7, -18>: C:=<2,-1,-3>:
M:=<x,y,z>: o:=<0,0,0>:
eq:=solve([seq(o[i] = (A-M + 2*(B-M) + 3*(C-M))[i], i=1..3)]);
point(T, -1/6, 7/3, -43/6...