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# what is the divergence of the

what is the divergence of the curl of a vector?

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- mathmanliuLv 71 decade agoFavorite Answer
(粗體字表向量)

以直角坐標而言,設F(x,y,z)=<F1, F2, F3>, F1~F3為純量函數R^3->R

curl(F)=<∂F3/∂y-∂F2/∂z, ∂F1/∂z-∂F3/∂x, ∂F2/∂x-∂F1/∂y>為向量函數

div[curl(F)]=∂(∂F3/∂y-∂F2/∂z)/∂x+∂(∂F1/∂z-∂F3/∂x)/∂y+∂(∂F2/∂x-∂F1/∂y)/∂z

若F(x,y,z)=<F1, F2, F3>為二階可微分函數=>div[curl(F)]=0

Source(s): me

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