I have three 3D points $A$, $B$ and $C$ which are defining a plane. If I want to get the equation of the plane, firstly I need its normal vector. Is it matter if I do it with $AB \times AC$ or $AC \times AB$? If it matters, why?
Thanks for your help!
I hope you know that $u\times v=-v\times u$, so cross multiplication is not commutative. So $AB \times AC$ and $AC \times AB$ will give you opposite normal vectors.
However, this should not affect your later work: any normal vector will do for this problem. So your intermediate calculations will change if you use the other cross product, but the end result will either be the same or will be equivalent (such as $x-2y-3z=4$ is equivalent to $-x+2y+3z=-4$).