(a) Let F₁ = x² 2 and F₂ = x x + y ŷ + z 2. Calculate the divergence and curl of F₁and F₂. Which one can be written as the gradient of a scalar? Find a scalarpotential that does the job. Which one can be written as the curl of a vector?Find a suitable vector potential.(b) Show that the field F3 = yz î + zx ŷ + xy 2 can be written both as the gradientof a scalar and as the curl of a vector. Find scalar and vector potentials for thisfunction.

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Answered: (a) Let F₁ = x² 2 and F₂ = x Ŷ + y ŷ +…

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(a) Let F₁ = x² 2 and F₂ = x Ŷ + y ŷ + z 2. Calculate the divergence and curl of F₁ 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.