Unformatted text preview: R be the projection of S onto the xyplane. Describe R , in terms of x and y . (b) Suppose that a thin plate in the shape of S has density ( x + y + z ) at each point ( x, y, z ). Find the mass of the plate. (Mass = ii S ( x + y + z ) dS .) 6. (a) Describe the surface S de²ned by: x = 3 cos θ , y = 3 sin θ , z = t , for θ : − π/ 2 → π/ 2 and t : 0 → 1. (b) Evaluate ii S xyz dS where S is the surface in part (a). 7. Prove that ∇· ( φ F ) = φ ∇· F + F ·∇ φ where φ = φ ( x, y, z ) and F is a vector ²eld in R 3 . Copyright c c 2012 The University of Sydney...
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 Three '09
 NOTSURE
 Statistics, Vector Calculus, Vector field

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