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:=:  B:=:  C:=:
M:=: o:=:
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); # put T by my hand
plane(P,2*x - y +z  + 1 = 0,[x,y,z]):

Problem. Let (P): 2x -y +2z + 9 = 0 be a plane and two points A(3,-1,2), B(1,-5,0). Find coordinates of the point M lies on (P) such that scalar product of two vectors MA and MB obtain  the minimum value. 

Plase write for me a code for the following problem:

Let (d): (x-1)/2 = (y+2)/1 = z/1 be a line and

(P): x + 2y -z - 3 = 0 be a plane.

Write the equation of the line (Delta) lies in the plane (P), perpendicular to the line (d) and the distance between (d) and (Delta) equal to sqrt(2).

Please write for me a code with following problem:

Write the equation of the plane wich passes through the two points A(2, -1, 0), B(0, 1, -2) and makes an angle 60 degrees with the plane x + 2y +z + 4 = 0.

Thank you very much.

Pease write for me a code with problem:

Find the equation of the plane (P1) which passes through the point M(1; 2; 3), perpendicular to the plane (P2): 5x -2y +5z + 10 = 0 and make an angle 45 degrees with the plane (P3): x - 4y -8z = 0.

Thank you very much.