Sorry if this is a basic question.
I have just started to realize this.
To find the normal of a plane we just take the cross product of any two vectors lying in the plane. However, depending on the order of the vectors in the cross product, we get two different vectors (opposite to each other) that are both normal to the plane.
Yet, when I also know that for a plane $ax+by+cz=d$, the normal vector is $(a,b,c)$.
What is so special about the equation of a plane that can identify/define the positive direction for the normal when a cross product of two vectors in the plane cannot?
I was thinking about the right-hand rule when doing the cross product but when a plane is arbitrary, which side do I view it from?
Thank you.