1. The problem statement, all variables and given/known data verify Stokes's theorem for the given surface and vector field. S is defined by x^2 + y^2 + z^2 = 4, z <= 4, oriented by downward normal; F = (2y-z, x + y^2 - z, 4y - 3x) 2. Relevant equations double integral over S of the curl F ds = integral over S' of F ds. 3. The attempt at a solution I calculated the curl F= del operator cross-product F = 5i - 2j - k, feel free to check if you wish. But in my vector calc book for a similar example, I noticed that they made an upward-pointing normal vector (as it was oriented upward) after del x F. I though del x F was a normal vector--am I wrong? The normal vector they came up with after the del x F (a separate calculation for my knowledge) was very different. Any hints from where to go from there?