# Question:How can I write a proc to write the equation of the planes passing two points and perpendicular to a given plane of a list planes?

## Question:How can I write a proc to write the equation of the planes passing two points and perpendicular to a given plane of a list planes?

I have a list
restart;
L := [10*x+y-6*z+66 = 0, 26*x-10*y-3*z+96 = 0, 2*x-y+6 = 0, 2*x-y+6 = 0, 4*x-5*y+3*z-6 = 0, 30*x-22*y+7*z+48 = 0, 2*x-2*y+z = 0, 26*x-19*y+6*z+42 = 0, 22*x-17*y+6*z+30 = 0, 14*x-30*y+23*z-96 = 0, 6*x-10*y+7*z-24 = 0, 2*x-7*y+6*z-30 = 0, 4*x-y-z+10 = 0, 42*x-2*y-19*z+20 = 0, 38*x-2*y-17*z+20 = 0, 30*x-y-14*z+10 = 0, 18*x+2*y-11*z-20 = 0, 6*x+13*y-16*z-130 = 0, 18*x+7*y-16*z-70 = 0, 6*x+2*y-5*z-20 = 0, 14*x+15*y-22*z-150 = 0, 18*x+13*y-22*z-130 = 0, 6*x+4*y-7*z-40 = 0, 26*x-3*y-10*z+110 = 0, 10*x-6*y+z+52 = 0, 2*x-z+8 = 0, 26*x+6*y-19*z+92 = 0, 22*x+6*y-17*z+76 = 0, 2*x+y-2*z+6 = 0, 14*x-18*y+11*z+92 = 0, 2*x-6*y+5*z+20 = 0, 2*x+6*y-7*z-4 = 0, 10*x-3*y-2*z+22 = 0, 26*x-7*y-6*z+66 = 0, 2*x-y = 0, y-z+11 = 0, 4*x-9*y+7*z-77 = 0, 6*x-5*y+2*z-22 = 0, 24*x-13*y+z-11 = 0, 2*x-y = 0, 2*x-y = 0, y-z+11 = 0, 4*x-5*y+3*z-33 = 0, 6*x-4*y+z-11 = 0, 4*x-3*y+z-11 = 0, 18*x-19*y+10*z-110 = 0, 14*x-13*y+6*z-66 = 0, 2*x-2*y+z-11 = 0, 26*x-6*y-7*z+68 = 0, 10*x-2*y-3*z+24 = 0, 2*x-z+2 = 0, 6*x+y-4*z-1 = 0, 4*x+y-3*z-3 = 0, y-z-7 = 0, 4*x+3*y-5*z-17 = 0, 18*x+10*y-19*z-52 = 0, 8*x+17*y-21*z-111 = 0, 4*x+5*y-7*z-31 = 0, 4*x-3*y+z-2 = 0, 10*x-6*y+z+4 = 0, 14*x-10*y+3*z-4 = 0, 26*x-15*y+2*z+14 = 0, 22*x-13*y+2*z+10 = 0, 18*x-26*y+17*z-84 = 0, 2*x-6*y+5*z-28 = 0, 38*x-6*y-13*z-16 = 0, 6*x-y-2*z-2 = 0, 18*x-2*y-7*z-16 = 0, 6*x+y-4*z-22 = 0, 6*x+y-4*z-22 = 0, 14*x+11*y-18*z-138 = 0, 2*x+y-2*z-14 = 0, 2*x+y-2*z-14 = 0, 22*x+2*y-13*z+40 = 0, 14*x+3*y-10*z+22 = 0, 2*x-2*y+z+8 = 0, 2*x-5*y+4*z+14 = 0, 2*x+5*y-6*z-6 = 0, 2*x-z+2 = 0, 6*x+y-4*z+8 = 0, 22*x-12*y+z-2 = 0, 8*x-9*y+5*z-10 = 0, y-z+2 = 0, y-z+11 = 0, 2*x-y-9 = 0, 8*x-3*y-z-25 = 0, 34*x-18*y+z-164 = 0, 18*x-10*y+z-92 = 0, 14*x-10*y+3*z-96 = 0, 28*x-17*y+3*z-159 = 0, 8*x-5*y+z-47 = 0, 2*x+3*y-4*z+29 = 0, 4*x-3*y+z-23 = 0, 32*x-15*y-z-103 = 0, 20*x-9*y-z-61 = 0, 10*x-6*y+z-44 = 0, 14*x-10*y+3*z-76 = 0, 2*x-2*y+z-16 = 0, 4*x-3*y+z-23 = 0, 12*x-19*y+13*z-89 = 0, 16*x-19*y+11*z-87 = 0, 20*x-3*y-7*z-73 = 0, 14*x-3*y-4*z-43 = 0, 4*x+3*y-5*z-47 = 0, 16*x-3*y-5*z-53 = 0, 22*x-2*y-9*z-92 = 0, 12*x+5*y-11*z-105 = 0, 16*x+3*y-11*z-107 = 0, 12*x+y-7*z-13 = 0, 6*x+y-4*z-7 = 0, 10*x-14*y+9*z+4 = 0, y-z-7 = 0, 2*x-z-7 = 0, 2*x+9*y-10*z-70 = 0, 18*x+y-10*z-70 = 0, 12*x+11*y-17*z-119 = 0, 2*x+y-2*z-14 = 0, 2*x-4*y+3*z+15 = 0, 4*x+y-3*z-15 = 0, 2*x-11*y+10*z+50 = 0, 14*x+3*y-10*z-50 = 0, 8*x+13*y-17*z-85 = 0, 4*x+13*y-15*z-75 = 0, 2*x+5*y-6*z-30 = 0, 12*x-7*y+z-101 = 0, 2*x-y-15 = 0, 6*x-4*y+z-56 = 0, 6*x-7*y+4*z-47 = 0, 8*x-7*y+3*z-51 = 0, 2*x-4*y+3*z-24 = 0, 6*x+y-4*z-46 = 0, 2*x+3*y-4*z-10 = 0, 2*x-z-16 = 0, y-z+2 = 0, 6*x-2*y-z-52 = 0, 10*x-2*y-3*z-84 = 0, 10*x+y-6*z-78 = 0, 2*x+y-2*z-14 = 0]

Now I want to write the equation of the planes passing two points A and B and perpendicular to all the equations of the above list. I can't to write a proc. With each plane of List, I tried
with(geom3d);
point(A, 1, 5, 3):
point(B, -2, -4, 3):
with(geom3d):
Equation(plane(P, L[5], [x, y, z])):
line(d, [A, B], t):
n1 := ParallelVector(d):
n2 := NormalVector(P):
with(linalg):
n3 := crossprod(n1, n2):
k := sort(primpart(lhs(Equation(plane(R, [A, n3], [x, y, z])))));
k*signum(lcoeff(k)) = 0