1. The problem statement, all variables and given/known data Let F =< yz + x, xz + 2x, xy + 3x >. Evaluate ∫F·dr where C is the intersection of the plane 2x + y − 3z = 0 and the sphere x2+ y2 + z2 = 4 oriented positively when viewed from above. 2. Relevant equations 3. The attempt at a solution The main question I have about this problem regards the normal vector of the surface. Because the surface is just an isolated portion of the plane, I thought I could use the normal vector of the plane to calculate the surface integral. However, when I try this I don't get the right answer. Can someone explain why this shouldn't work and what the right way would be to find the normal vector? Thanks!