(a) div F (b) curl F 2. Let F(r, y, z) = (x, y, z) and let g(x, y, z) |F(x, y, z)|. Find values of a, b, c, and m that satisfy the following: %3D (a) div F = a (b) V (gF) =bg (c) |curl (gF)| = c (d) V² (9*) = m g Note: Vf = div(Vf) = V · (Vf) = faz + Syy + fzz is the Laplacian of f. 3. Let F(r, y, z) = P(x, y, z)i+ Q(x,y, z)j+ R(x, y, z)k. The vector Laplacian oper- ator is defined as V°F = V (V · F) – V × (V × F). This is a rather involved definition that can be simplified. By expanding the right-hand side of this equation, show that an equivalent definition of the vector Laplacian operator is V°F = (V°P) i+ (v²Q)j+(V°R)k. 4. Find the surface area of the portion of the paraboloid r = 4 - y - 2 that lies between the cylinders y?+ 22 = 1 and y? + 22 = 4. Over

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A: The given expression is 1+1(9)-20 When we multiply any number by 1 the result is 1. So when we…

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A:

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A: 3-4+8 =-1+8 =8-1 7

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A: NOTE: Refresh your page if you can't see any equations. . add 13 to both sides

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A: Use PEMDAS rule to simplify.First we work with the parenthesis. In it 8-12=-4

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A: I am going to solve the given problem by using some simple algebra to get the required result.