Show that the vector field defined by Fሬ⃗ = 2xyz ଷ ⃗ı + x ଶ z ଷ ⃗ȷ + 3x ଶyz ଶkሬ⃗ is irrotational. Find also the scalar ∅ such that Fሬ⃗ = grad ∅.

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