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Describe the gradient of a function of 3 variables

  1. Mar 15, 2014 #1

    kosovo dave

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    1. The problem statement, all variables and given/known data

    Match the function with the description of its gradient.

    2. Relevant equations
    f(x,y,z)=√(x^2+y^2+z^2)
    1. constant, parallel to xy plane
    2. constant, parallel to xz plane
    3. constant, parallel to yz plane
    4. radial, increasing in magnitude away from the origin
    5. radial, constant magnitude
    6. radial, decreasing in magnitude away from origin

    3. The attempt at a solution
    grad f(x,y,z)=(df/dx)i+(df/dy)j+(df/dz)k
    grad f=[(x^2+y^2+z^2)^-.5](xi+yj+zk)

    I know it's definitely radial. I found a solution online that said the magnitude was constant though, and I can't tell why.
     
  2. jcsd
  3. Mar 15, 2014 #2

    Dick

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    Well, what is the magnitude of the grad f you computed? What the magnitude of (xi+yj+zk)?
     
  4. Mar 15, 2014 #3

    kosovo dave

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    Oh I think I get it now. I'd end up with sqrt(x^2+y^2+z^2)/sqrt(x^2+y^2+z^2) just leaving the vector i+j+k?
     
  5. Mar 15, 2014 #4

    Dick

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    Almost, you want to find |grad f|. You replaced the vector with its magnitude. You are left with just 1.
     
  6. Mar 15, 2014 #5

    kosovo dave

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    Clear as the Mississippi! Just kidding. I get it now. Thanks for the help, Dick!
     
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