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):**