We introduce the vector differential operator ∇ (“del”) as
∇=i∂x∂+j∂y∂+k∂z∂ Then for the vector field F
curlF=∇×F
divF=∇⋅FThe cross product ∇×F is perpendicular to both ∇ and F.
Hence for any vector field F
∇⋅(∇×F)=0 Therefore for any vector field F
div(curlF)=∇⋅(∇×F)=0
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