I wish to find a normal vector to the surface given by the interior of the intersection of the cylinder $x^2+y^2=1$ and the plane $x-z=1$. I'm not entirely sure the best way to go about finding a normal vector without parametrizing the surface (which doesn't seem like the best way to go).
I thought to try and use the gradient to find a normal vector but I couldn't figure out exactly what $f(x,y,z)$ I would need to take the gradient of, (and also I would need a point on the surface to find a normal vector at that point).
Any help?