Consider the vector field F: R³ → R³ defined by F(x, y, z)=(x² - y², -2xy, z). a) Show that F is a gradient field by verifying that curl(F) = (0,0,0). b) Find a function f: R³ R such that Vf(x, y, z) = F(x, y, z). c) Compute fF.dr where C is a curve with the initial point (1,0,-1) and the terminal point (2,1,0).

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