I want to write the equation of the plane passing through the three points A, B, C has the form ax + by + cz + d = 0 where a, b, c, d are integer numbers, a >0 if a <> 0; b>0 if a = 0 and b<>0,...and igcd(a, b, c) = 1.

If the coordinates of the vertices A, B, C are all integers, for example A(2,2,2), B(1,2, -1), C(1,-1,-4), I tried,

with(geom3d):

point(A,2,2,2):

point(B,1,2, -1):

I want to find a triangle with the vertices A(x1, y1, z1), B(x2, y2, z2), C(x3, y3, z3) knowing that the point G(1,1,1) is centroid of the triagle ABC and x1, y1, z1, x2, y2, z2, x3, y3, z3 are integer numbers, but I can not find. How do I tell Maple to do that? 

I have a list L. In geom3d, I want to write all tangent of plane of the sphere S from L. But I don't know. I only write one point . I tried 

> restart:

with(geom3d):

L:=[[-5, -5, 8], [-5, -1, 10], [-5, 3, 10], [-5, 7, 8], [-5, 8, -5], [-5, 8, 7], [-5, 10, -1], [-5, 10, 3], [-1, -5, 10], [-1, 7, 10], [-1, 10, -5], [-1, 10, 7...

I want to solve the equation f(f(-1))=sqrt(2)+g(f(2)), where

f:=x->a/x^2-3*x+2 and g:=x->a*sin(2*x), a is an unknow. I tried

restart:
f:=x->a/x^2-3*x+2:
g:=x->a*sin(2*x):
solve(f(f(-1))=sqrt(2)+g(f(2)),a):
evalf(%);

and receive 13.02210936+4.135282756*I. 

I have a list [1, 2, 3, 11, 29, 88, 252, 739, 2146, 6257, 18213, 53051, 154484, 449908, 1310217, 3815674, 11112091, 32360987, 94242573, 274456016]. How to select all even numbers of this list?