Results 1 to 2 of 2

Math Help - [SOLVED] vector identity proof

  1. #1
    sam1986
    Guest

    [SOLVED] vector identity proof

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    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
    Last edited by CaptainBlack; August 26th 2006 at 09:53 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. vector identity
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 27th 2010, 06:45 PM
  2. Replies: 2
    Last Post: May 29th 2009, 12:41 AM
  3. Replies: 0
    Last Post: February 21st 2009, 10:40 AM
  4. [SOLVED] Vector Proof
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 13th 2008, 02:38 PM
  5. Vector Identity
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: May 16th 2007, 08:00 AM

/mathhelpforum @mathhelpforum