My question is about how to define the bounds for the integral. given a vector field $F$ and a triangle with vertices $(1,2,3), (4,5,6),(7,8,9)$. how to define the bounds when integrating the vector field?
here is what my approach:
I take a vertices as origin, and find the $2$ vectors by taking the other $2$ vertices and subtracting the origin point. then, I take cross-product with these $2$ vectors, to find the normal vector. and then I use dot-product with the normal vector and $(x,y,z)$, and set it equal to $0$, to find the equation of a plane that contains this triangle.
I don't know what to do after i found the equation of the plane. if anybody would give me a hint, that would be so nice. thanks!
