Question: 5. Consider the vector field F(x, y, z) = = (a) Prove that F is not a gradient field. (b) Show that F curl(F)

5. Consider the vector field F(x, y, z) = = (a) Prove

5. Consider the vector field F(x, y, z) = = (a) Prove that F is not a gradient field. (b) Show that F curl(F) = 0. 2y2zi+4yzj+2y2k. (c) Find a function = (x) satisfying curl (pF) (c) Find a potential function f(x, y, z) such that (14=3+3+4+4 p- = 0 with (1) = 1. F = Vf.

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