What is the purpose of using the nabla operator in this equation?

[curupira]

A simple question:
In a homework I find :
F1 X nabla X F2 where X is the simbol of cross product

I know that AX(BXC)= (A*C)*B-(A*B)C

Where* here is used to divergence

In the next step it was:

-Nabla*(F2)F1 + nabla(F1*F2)

I don't understant it, why?

 

[curupira]

The basic idea is What the diference F*nabla and Nabla*F

 

[DrGreg]

The basic idea is What the diference F*nabla and Nabla*F

$(\textbf{F} \cdot \nabla) \textbf{G}$ is a vector whose ith component is

$$\left[ (\textbf{F} \cdot \nabla) \textbf{G} \right]_i = \sum_j F_j \frac{\partial G_i}{\partial x_j}$$​

whereas

$$\left[ (\nabla \cdot \textbf{F}) \textbf{G} \right]_i = \sum_j \frac{\partial F_j}{\partial x_j} G_i$$​

 

[Danger]

Jeez, man! Will you please stop posting homework questions in the wrong places?