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Math Help - Find ∇||r||

  1. #1
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    Find ∇||r||

    Hello.
    How to find ∇||r||, r=xi +yj +zk
    .
    My first step:
    ||r||^2 = rr
    then don't know how to continue.

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  2. #2
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    Re: Find ∇||r||

    Hey happymatthematics.

    Hint: Note that in R^3, r.r = x^2 + y^2 + z^2. With grad = (d/dx,d/dy,d/dz) you need to apply each differential operator to ||r|| to get the answer. (Think about differentiating SQRT(x^2 + y^2 + z^2) with respect to each variable).
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  3. #3
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    Re: Find ∇||r||

    Find ∇||r||-delta_r_suffix-notation.png
    I've tried the method you told me, but
    haha, My teacher required us to use suffix notation.
    Can you teach me how to solve this problem with suffix notation?
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  4. #4
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    Re: Find ∇||r||

    The RHS will be ||r||^2 = x^2 + y^2 + z^2.
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  5. #5
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    Re: Find ∇||r||

    but how to represent ||r||^2 = x^2 + y^2 + z^2 in suffix notation?
    or how to find ∇||r|| using suffix notation?
    Last edited by happymatthematics; February 1st 2013 at 10:58 PM.
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  6. #6
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    Re: Find ∇||r||

    Do you mean differentiating in terms of d/d||r||? If this is the case you need to use the chain rule where ||r|| = f(x,y,z) and then link d/dr to d/dx, d/dy, and d/dz.

    Remember that d/dr(r^2) = 2r.
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  7. #7
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    Re: Find ∇||r||

    Is d/dr ||r|| = ∇||r|| ?
    and is d/dr (rr) = ∂i (ri ri) ?

    Last edited by happymatthematics; February 1st 2013 at 11:14 PM.
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  8. #8
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    Re: Find ∇||r||

    I may agree with you but I have to ask what your definition of r is with respect to the derivative (and also how you link r with x,y,z in terms of the derivatives and the chain rule)?
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  9. #9
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    Re: Find ∇||r||

    r=(x,y,z)
    but can I use r (a vector) to be a variable in differentiation?
    d/dr seems strange
    Last edited by happymatthematics; February 1st 2013 at 11:35 PM.
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  10. #10
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    Re: Find ∇||r||

    You can, but you have to define the mapping.

    It may not seem intuitive but all that is happening is that you are dealing with a multi-variable situation that is mapping things between elements of a vector.

    With the grad operator you have a vector definition (d/dx,d/dy,d/dz) and you are simply mapping things to different elements of a vector.

    The general derivative operator for a multi-variable scenario is just a matrix of derivatives which also happens to be a linear object.
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  11. #11
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    Re: Find ∇||r||

    I've asked my classmate and she said the professor will send us the solution tomorrow. haha.
    Thank you chiro.
    Sorry for wasting your time!!
    I think suffix notation is my enemy!!
    I lack mathematics intuition and inspiration, but I will work hard!
    Last edited by happymatthematics; February 1st 2013 at 11:44 PM.
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