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Separation vector

  1. Jan 18, 2005 #1
    Let c' be the separation vector from a fixed point(x'',y'',z'') to the point (x,y,z) and let c be its length. show that

    Gradient(1/c) = -c'(hat)/c^2

    Thnaks for the help
     
  2. jcsd
  3. Jan 18, 2005 #2

    cronxeh

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    Gold Member

    your work?
     
  4. Jun 25, 2008 #3
    begin by writing 1/c in terms of cartesian coordinates.

    c = sqrt[(x - x`)^2 + (y - y`)^2 + (z - z`)^2]
    1/c = ?

    then differentiate using multiple applications of the chain rule. Remember that the primed terms are constant when differentiating respect to x, y or z. This was the part that confused me at the beginning as I didn't know how to differentiate those.
     
  5. Jun 28, 2008 #4
    What is "hat"?
     
  6. Jun 28, 2008 #5

    tiny-tim

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    Science Advisor
    Homework Helper

    ^

    "hat" is ^

    it means the unit vector in the direction of c' :smile:
     
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