- #1

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**Statement:**

I was wondering if the following are identical,

[tex]\nabla \bullet \nabla \times \vec{A} = \nabla \bullet (\nabla \times \vec{A}) ?[/tex] (#1)

Also, more importantly I was wondering if someone could explain to me why the following is zero for any vector,

[tex]\nabla \bullet \nabla \times \vec{A} = 0?[/tex]

**Reasoning:**

If we look at [tex]\nabla \bullet \nabla \times \vec{A}[/tex], Isn't [tex]\nabla \bullet \nabla[/tex] the laplacian, or [tex]\nabla^{2}?[/tex] Is that the reason we cannot perform the operation in equation (#1) above- the laplacian is a function that needs a vector field to be operated on, and there is none. So [tex]\nabla \bullet \nabla = 0.[/tex]

Thanks, alot,

JL