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## Homework Statement

Let [tex]\mathbf{G}(x,y,z)[/tex] be an irrotational vector field and g(x,y,z) a [tex]C^1[/tex] function. Use vector identities to simplify:

[tex]\nabla\cdot(g\nabla \times (g\mathbf{G})) [/tex]

## Homework Equations

The '14 basic vector identities'

## The Attempt at a Solution

I tried using the identity [tex]\nabla\cdot(\mathbf{F} \times \mathbf{G}) = \mathbf{G}\cdot(\nabla\times\mathbf{F}) - \mathbf{F}\cdot(\nabla\times\mathbf{G})[/tex]

But I'm not sure if i can treat [tex] g\nabla [/tex] as a vector?

Really I'm quite clueless.