[SOLVED] [SOLVED] vector identity proof

Quote:

Originally Posted by sam1986

Need help proving this
let f(x,y,z) and g(x,y,z) be any C^2 scaler functions. Without using the basic identities of vector analysis prove that

grad.(fgradg-ggradf)=fgrad^2g- ggrad^2f

(ive put grad instead of the upside down triangle symbol)

thanks

To start you off:

$\nabla.(f \nabla g-g \nabla f)=\sum_i \frac{\partial}{\partial x_i}$ $<br /> (f \nabla g-g \nabla f)_i$ $<br /> =\sum_i \frac{\partial}{\partial x_i} \left( f\frac{\partial g}{\partial x_i}-g\frac{\partial f}{\partial x_i}\right)<br />$

Now apply the product rule to the what is inside the right most summation
and simplify and you should have what you want.

RonL