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Find the grad (vector calculus)

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data

    show that
    grad(r.[tex]\hat{k}[/tex]/r^3) = [r^2[tex]\hat{k}[/tex]-3(r.[tex]\hat{k}[/tex])r]/r^5

    2. Relevant equations

    3. The attempt at a solution

    I know that r=xi+yj+zk
    and i know how to calculate the grad from the formula but, what is r.[tex]\hat{k}[/tex] ?
    thank you
  2. jcsd
  3. Dec 7, 2008 #2


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    Science Advisor
    Homework Helper

    r.k=z. So you can just show it directly by showing both sides are equal. But actually that formula holds for any constant vector 'k'. If f is a scalar function (like r.k) and g is a scalar function (like r^3), grad(f/g)=grad(f)/g-f*grad(g)/g^2. That's what the two different terms on the right side are.
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