Question: For the vector field F(x, y, z) = (xy2 , yz2 , zx2 ) and the unit sphere S = {(x, y, z) | x

For the vector field F(x, y, z) = (xy2 , yz2 , zx2 ) and the unit sphere S = {(x, y, z) | x 2 + y 2 + z 2 = 1}, calculate the flux of F through S in the outward direction by Gauss' Theorem.

(b) For the vector field F(x, y, z) = (xy?, yz2, zx2) and the unit sphere S = {(x, y, z) | x2 + y" + 2" = 1}, calculate the flux of F through S in the outward direction by Gauss' Theorem. (c) For the same vector field F(x, y, z) = (xy?, yz2, zx2) as in (b), calculate V X F

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