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Let G denote the sphere of radius 1, which can be parameterized by r(0, $) = (sin ocos 0, sin osin 0, coso) 050 5 2x,0Sosn The Jacobian of this map is dS = sin o de do. Note that the the normal vector on this sphere is n(r, y, z) = (x, y, z) = n(0, $) = (sin ocos 0, sin o sin 0, cos o) For the problems below, set F(x, y, z) = (-y, x, 52). 1. Compute F . n dS directly using the parameterization described above. 2. Now compute F . n dS using the Divergence Theorem 3. Now let H denote the top half of G, H = {(x, y, z)|x2 + y? + 22 = 1, > > 0}. Use Stokes' Theorem to compute curlF . n ds