Solution: Let F be the vector field (x^2+y^2+z^2)< x, y, z> and S be the sphere centred at the origin with radius a and normal vectors pointing away from
Question: (3 points) Let \(\mathrm{F}\) be the vector field
\[\left(x^{2}+y^{2}+z^{2}\right)\langle x, y, z\rangle\]and \(S\) be the sphere centred at the origin with radius \(a\) and normal vectors pointing away from the origin. Find
\[\iint_{S} \mathbf{F} \cdot d \mathbf{S}\]both directly and by using the Divergence theorem.
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