Results 1 to 4 of 4

Math Help - Question in Curl of a cross product.

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    58

    Question in Curl of a cross product.

    \nabla X (\vec A X \vec B) \;=\; (\vec B \cdot \nabla)\vec A - \vec B(\nabla \cdot \vec A) -(\vec A \cdot \nabla)\vec B + \vec A ( \nabla \cdot \vec B) .

    What is  \vec A \cdot \nabla ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,832
    Thanks
    1602
    Have they told you what \displaystyle \mathbf{A} and \displaystyle \mathbf{B} are equal to?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    58
    Quote Originally Posted by Prove It View Post
    Have they told you what \displaystyle \mathbf{A} and \displaystyle \mathbf{B} are equal to?
    Nop, this is just a general formula of the product of two vectors.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    Quote Originally Posted by yungman View Post
    \nabla X (\vec A X \vec B) \;=\; (\vec B \cdot \nabla)\vec A - \vec B(\nabla \cdot \vec A) -(\vec A \cdot \nabla)\vec B + \vec A ( \nabla \cdot \vec B) .

    What is  \vec A \cdot \nabla ?
    It's the vector \vec{A} dotted with the gradient operator. The result of this dot product is a scalar operator. So, for example, the expression

    \displaystyle(\vec{A}\cdot\nabla)\vec{B}=\left(\su  m_{j=1}^{3}A_{j}\,\dfrac{\partial}{\partial x_{j}}\right)\vec{B}=\left\langle\sum_{j=1}^{3}A_{  j}\,\dfrac{\partial B_{1}}{\partial x_{j}},\sum_{j=1}^{3}A_{j}\,\dfrac{\partial B_{2}}{\partial x_{j}},\sum_{j=1}^{3}A_{j}\,\dfrac{\partial B_{3}}{\partial x_{j}}\right\rangle.

    Does that make sense?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: September 2nd 2009, 05:07 AM
  2. another cross product question..
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: August 22nd 2009, 01:20 AM
  3. cross product question of j ,k ..
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: August 22nd 2009, 01:02 AM
  4. cross product question
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: May 22nd 2009, 01:38 PM
  5. Replies: 1
    Last Post: May 14th 2008, 12:31 PM

Search Tags


/mathhelpforum @mathhelpforum