(a) Let F1 = x²î and F2 x+ yŷ +z2. Calculate the divergence and curl ofF and F2. Which one can be written as the gradient of a scalar? Find a scalar potential that does the job. Which one can be written as the curl of a vector?Find a suitable vector potential. (b) Show that F; = yzâ+ zx ŷ + xy2 can be written both as the gradient of a scalar and as the curl of a vector. Find scalar and vector potentials for this function.

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