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Thread: Verify the Identity

  1. #1
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    Verify the Identity

    Let vector r = xi + yj + zk and r = |vector r|

    Verify that ∇ • vector r = 3.

    Must I take the partial derivative with respect to x, y, and z individually?

    If so, then ∇• vector r = 1 + 1 + 1 = 3.

    I do not understand why r = |vector r| is given in this problem.
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  2. #2
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    Re: Verify the Identity

    Quote Originally Posted by USNAVY View Post
    Let vector r = xi + yj + zk and r = |vector r|
    Verify that ∇ • vector r = 3.
    Must I take the partial derivative with respect to x, y, and z individually?
    If so, then ∇• vector r = 1 + 1 + 1 = 3.
    I do not understand why r = |vector r| is given in this problem.
    Do you understand that $\nabla = i\frac{\partial }{{\partial x}} + j\frac{\partial }{{\partial y}} + k\frac{\partial }{{\partial z}}$
    If you know how to do dot products then : $\nabla \cdot r = x\left( {\frac{\partial }{{\partial x}}} \right) + y\left( {\frac{\partial }{{\partial y}}} \right) + z\left( {\frac{\partial }{{\partial z}}} \right) = 1 + 1 + 1$
    Thanks from USNAVY
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  3. #3
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    Re: Verify the Identity

    Quote Originally Posted by Plato View Post
    Do you understand that $\nabla = i\frac{\partial }{{\partial x}} + j\frac{\partial }{{\partial y}} + k\frac{\partial }{{\partial z}}$
    If you know how to do dot products then : $\nabla \cdot r = x\left( {\frac{\partial }{{\partial x}}} \right) + y\left( {\frac{\partial }{{\partial y}}} \right) + z\left( {\frac{\partial }{{\partial z}}} \right) = 1 + 1 + 1$
    This means I was right.
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  4. #4
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    Re: Verify the Identity

    I do not understand why r = |vector r| is given in this problem.
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  5. #5
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    Re: Verify the Identity

    I suspect that there is some other part of the problem that involved \left|\vec{r}\right|.
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