I want to write the equation of the plane which equidistant the two the planes P and Q. This is my code

restart:

with(geom3d):

plane(P,2*x+3*y-6*z+1=0,[x,y,z]):

plane(Q,x -4*y-8*z+1=0,[x,y,z]):

point(M,x,y,z):

E:=distance(M,P)- distance(M,Q);

simplify(%);

but, i can simplify(E). Please help me.

The triangle ABC with A(4,7,5),  B(3,7,-2),  C(0,2,2) is a equilateral triangle. How do i find coordinates vertices of a equilateral triangle which their coodinates are integer numbers? Please help me. Thank you very much.

In geom3d, i have equation a plane. Now i want to get two points A and B in the plane P and write the equation of the line which passing two point A, B. 

restart:
with(geom3d):
plane(P, 2*x + 2*y -z + 4=0,[x,y,z]):

f := (a,b,c) -> eval(lhs(Equation(P)), [x=a,y=b,z=c]): 

T:=f(-1,2, a):
eq:=solve(T=0,a): coordinates(point(A,-1,2,eq)):

We have 1^2 + 2^2 +2^2 = 3^2; 2^2 + 3^2 + 6^2 = 7^2; 2^2 + 10^2 +11^2 = 15^2. Please write for me a command solve the equation a^2 + b^2 + c^2 = d^2, where, a, b, c, d are integer numbers, and d <=100. Thank you very much.

In geom3d, how i can subs coordinates of a point M(t+1, t - 2, t+ 3) into equation of a plane (P) has equation x + 2*y -3*z + 1 = 0? Please help me.