Orientation of a 3D triangle vertices

Question

I have a 3D triangle which represent a plane. How to determine whether the vertices are oriented clockwise or anti clockwise. I need this because I'm calculating normal for triangle which resides on a plane and depending on the orientation the direction of the normal of the plane changes. Like if the triangle resides on a plane where z = 0, then the normal could be (0,0,1) or (0,0,-1).

Answer 1

Counterclockwise in $\mathbb{R}^3$ already presumes a choice of normal direction.

The reason counterclockwise is determined for the $xy$-plane is because, regarding it as the plane $z=0\;$in $\mathbb{R}^3$, we implicitly assume an upwards directed normal vector (i.e., we view the plane from above).

So if you choose a normal vector for your plane, you can define counterclockwise as "counterclockwise from above", where "above" is based on the chosen normal direction.

In a given context, there may be a natural choice of normal direction, but otherwise, there are two possible directions, and the choice is arbitrary.