2. Define a surface S = {x+y+z 49, -7sz ...

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2. Define a surface S = {x+y+z 49, -7sz<7//2 }. This is a spherical surface with some of the top sliced off. (A sketch will really help.) Let the unit surface normal vector n that we use in our integral be oriented so that it points "away" from the origin, Define the path C as the boundary of S. NOTE: The direction of path C and the direction of [- 3y normal vector n are related as described in Stokes's Theorem. Define a vector field F(r)= 3x 3z (a) Evaluate the surface integral [f(V x F)• n dA directly. (The path integral using Stokes's Theorem will be caleulated in the next part) (b) Now use Stokes's Theorem to evaluate the same integral. In other words, evaluate (F• dr. Orient the direction of path C so that is consistent with the normal vector n of S. (By Stokes's Theorem, you should get the same answer as part (a).) 2. Define a surface S = {x+y+z 49, -7sz<7//2 }. This is a spherical surface with some of the top sliced off. (A sketch will really help.) Let the unit surface normal vector n that we use in our integral be oriented so that it points "away" from the origin, Define the path C as the boundary of S. NOTE: The direction of path C and the direction of [- 3y normal vector n are related as described in Stokes's Theorem. Define a vector field F(r)= 3x 3z (a) Evaluate the surface integral [f(V x F)• n dA directly. (The path integral using Stokes's Theorem will be caleulated in the next part) (b) Now use Stokes's Theorem to evaluate the same integral. In other words, evaluate (F• dr. Orient the direction of path C so that is consistent with the normal vector n of S. (By Stokes's Theorem, you should get the same answer as part (a).)

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