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Homework Help: Divergence of a variable vector

  1. May 14, 2008 #1
    1. The problem statement, all variables and given/known data

    v = (a.r)r where r=xi+yj+zk and a is a constant vector
    show [tex]\nabla[/tex].v = 4(a.r)

    I let a= ai+bJ+ck

    then (a.r) = ax+by+cz

    then this (a.r)r = ax[tex]^{2}[/tex]i+by[tex]^{2}[/tex]j+cz[tex]^{2}[/tex]k

    [tex]\nabla[/tex].v = da1/dx+da2/dz+da3/dz =2ax+2by+2cz

    which is equal to 2(a.r)

    am i wrong or the book?
  2. jcsd
  3. May 14, 2008 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    This is not true. For example, consider the scalar [itex]\lambda[/itex],

    [tex]\lambda\left(x\hat{i}+y\hat{j}+z\hat{k}\right) = \left(\lambda x\hat{i}+ \lambda y\hat{j}+\lambda z\hat{k}\right)[/tex]

    And in your case,

    [tex]\lambda = ax+by+cz[/tex]
  4. May 14, 2008 #3
    got ya, thanks a million
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