Question: Coordinates of a point (10)

Problem. In the plane 2*x -3*y +3*z -17 = 0, find a point M such that the sum of its distances from the poits A(3, -4, 7) and B(-5, -14, 17) will have the least value.

First way.

restart:with(geom3d):

point(A,3,-4,7):

point(B,-5,-14,17):

plane(P,2*x - 3*y +3*z -17=0,[x,y,z]):

reflection(Q,A,P):

line(BQ,[B,Q]):

coordinates(intersection(M,BQ,P));

 

I can not solve by second way

restart: with(LinearAlgebra):

A:=<3,-4,7>:

B:=<-5,-14,17>:

M:=<x,y,z>:

d:=Norm(A-M,2) + Norm(B-M,2):

extrema(d,{2*x - 3*y +3*z -17=0},{x,y,z},'s'),  s;

Please help me. Thank you.




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