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Homework Help: Short (I think) vector calculus question

  1. Feb 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Calculate the following expressions:

    question.png

    2. Relevant equations

    3. The attempt at a solution

    Letting the vector a = (a_1, a_2, a_3) I've worked out that it's 2|a|^2

    While that method is fairly quick, I don't particularly like it, and was wondering if there is a shorter or neater method using identities and such, perhaps using del^2 = del . del, then using div and grad identities? Cheers.
     
  2. jcsd
  3. Feb 20, 2012 #2

    Dick

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    You could work it out as div(grad((a.r)^2)), but it amounts to doing the pretty much the same thing you just did.
     
  4. Feb 21, 2012 #3
    Yeah, that's what I thought. But wasn't sure if there was a way to simplify grad((a.r)^2)
     
  5. Feb 21, 2012 #4

    Dick

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    grad((a.r)^2)=2(a.r)*grad(a.r)=2(a.r)a. div(2(a.r)a)=a.grad(2(a.r))+2(a.r)div(a)=2a.a+0=2a.a. You can write down all the steps with vectors, but I really don't think it's saving much time.
     
    Last edited: Feb 21, 2012
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