How do you find the parametric equation for a plane as would be used in a Line Integral?
AKA
How would you take the equation x+y+z=2 and form that into an r(t) equation?
Once again, this makes no sense. An entire plane is NOT a "portion" and does not have a boundary to apply Stoke's theorem to. I suspect that you have some region in the plane x+ y+ z= 1 that actually has a boundary and it is that boundary you want to integrate around and want parametric equations for.
I can only second mr fantastic's plea that you post the entire problem. Until we know what region and what boundary you are talking about, we cannot help you.