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Math Help - Proving vector calculus relationships

  1. #1
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    Proving vector calculus relationships

    How would you go about proving:

    Curl(f(r)R) where R is the position vector x^(2)i +y^(2)j +z^(2)k

    I know it should equal zero but once Ihave it in its components I am struggling to make them equal zero.

    Thank you
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Proving vector calculus relationships

    so basically the curl is evaluates to \begin{bmatrix}\frac{\partial}{\partial{y}}z^2 -  \frac{\partial}{\partial{z}}y^2 \\ \frac{\partial}{\partial{x}}z^2 -  \frac{\partial}{\partial{z}}x^2 \\ \frac{\partial}{\partial{x}}y^2 -  \frac{\partial}{\partial{y}}x^2 \end{bmatrix} which is clearly  \begin{bmatrix} 0\\0\\0 \end{bmatrix}
    Last edited by jakncoke; February 7th 2013 at 10:53 PM.
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  3. #3
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    Re: Proving vector calculus relationships

    Trianagt, to use jakncokes' answer you will also need to know that \nabla\times (f\vec{v})= \nabla f\times v+ f\nabla\times v
    Last edited by HallsofIvy; February 8th 2013 at 05:38 AM.
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