1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Expression with two vectors and del operator

  1. Sep 21, 2012 #1
    1. The problem statement, all variables and given/known data
    (A.∇)B



    What does this mean and how do I go about trying to expand this (using cartesian components)?
     
  2. jcsd
  3. Sep 21, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Well, [itex]\displaystyle \vec{\text{A}}\cdot\vec{\nabla}=\text{A}_x\,\frac{ \partial}{\partial x}+\text{A}_y\,\frac{ \partial}{\partial y}+\text{A}_z\,\frac{ \partial}{\partial z}\ .
    [/itex]

    So that [itex]\displaystyle \left(\vec{\text{A}}\cdot\vec{\nabla}\right) \vec{\text{B}}=\text{A}_x\,\frac{ \partial\vec{\text{B}}}{\partial x}+\text{A}_y\,\frac{ \partial\vec{\text{B}}}{\partial y}+\text{A}_z\,\frac{ \partial\vec{\text{B}}}{\partial z}\ .
    [/itex]
     
  4. Sep 21, 2012 #3
    Of course. It was the order (A.∇) rather than (∇.A) that confused me but now I realise that these are obviously equivalent. Thanks
     
  5. Sep 21, 2012 #4
    Actually that's wrong isn't it?
    If the order is reversed you find the derivatives of each component of A. In the problem case though the derivation is carried out on the components of B. I hope this is right as it makes sense in my head.
     
  6. Sep 21, 2012 #5

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Yes, it's correct. The whole expression is called the derivative of B along A.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Expression with two vectors and del operator
  1. Del operator (Replies: 7)

Loading...