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Del operator

  1. Apr 21, 2014 #1
    f(x,y,z) = x2 + y2 + z2

    which values of x,y,z does ∇f point in the positive z direction


    ok so I know ∇f = i ∂/∂x + j ∂/∂y + k ∂/∂z

    which turns out to be

    ∇f = 2x i + 2y j + 2z k

    but how am I finding values so that z points in the positive direction? what does that even mean?
    ∇f is gradient, could it have specified x direction or y direction, if so what would differ about how to answer the question?

    any help/explanation much appreciated
     
  2. jcsd
  3. Apr 21, 2014 #2

    micromass

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    I guess they mean that a vector points in the positive ##z##-direction if it is of the form ##(0,0,k)## for ##k>0##. Does that help?
     
  4. Apr 21, 2014 #3
    I don't recognise this kind of question, how would I go about finding this vector?
     
  5. Apr 21, 2014 #4

    micromass

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    For which ##(x,y,z)## is the gradient ##(2x,2y,2z)## of the form ##(0,0,k)## for ##k>0##.
     
  6. Apr 21, 2014 #5
    is it as simple as follows:
    x = 0
    y= 0
    z = any positive integer?
     
  7. Apr 21, 2014 #6

    micromass

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  8. Apr 21, 2014 #7

    LCKurtz

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    Almost. You mean any positive number.
     
  9. Apr 21, 2014 #8
    Thank you for the help, it really is appreciated!
     
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