Question: (problem4.19 from Spivak's book) The gradient for a vector field vecF=(F1,dots,Fn)is defined bygrad(vec(F))=delF1delx1vec(e)1+cdots+partialFFndelxnvec(e)nIn what follows, we take n=3,vec(F) smooth, and define the following formsvec(F)1=F1dx+F2dy+F3dzandvec(F)2=F1dy??dz+F2dz??dx+F3dx??dy(a) Show

(problem4.19 from Spivak's book) The gradient for a vector field vecF=(F1,dots,Fn)is defined bygrad(vec(F))=delF1delx1vec(e)1+cdots+partialFFndelxnvec(e)nIn what follows, we take n=3,vec(F) smooth, and define the following formsvec(F)1=F1dx+F2dy+F3dzandvec(F)2=F1dy??dz+F2dz??dx+F3dx??dy(a) Show thatdf=gradvec(F)1

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