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## Homework Statement

The vectors

**F**and

**G**are arbitrary functions of position. Starting w/ the relations

**F**x (∇ x

**G**) and

**G**x (∇ x

**F**), obtain the identity

∇(

**F**.

**G**) = (

**F**. ∇)

**G**+ (

**G**. ∇)

**F**+

**F**x (∇ x

**G**) +

**G**x (∇ x

**F**)

## Homework Equations

## The Attempt at a Solution

I started off with the relation

**F**x (∇ x

**G**) and used the BAC-CAB rule:

**F**x (∇ x

**G**) = ∇(

**F**.

**G**) - (

**G**. ∇)

**F**

so ∇(

**F**.

**G**= (

**G**. ∇)

**F**+

**F**x (∇ x

**G**) which seems to contradict the identity I am supposed to get. What am I doing wrong?