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Math Help - Vector Operations

  1. #1
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    Vector Operations

    Can somebody check the following answers are correct and give any guidance on the others?

    I was given F = (x^3, By^2, xyz)

    (i) del.F = 3x^2 + 2By + xy

    (ii) del.(del.F) = 6x + 2B // Differentiating (i)

    (iii) del x F = (xz)i - (yz)j

    (iv) del x (del x F)
    Not sure how to do this?

    (v) del^2(F)
    Do you just differentiate F twice wrt x,y,z and then add them?

    (vi) (F.del).F
    Summation convention?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Yerobi View Post
    Can somebody check the following answers are correct and give any guidance on the others?

    I was given F = (x^3, By^2, xyz)

    (i) del.F = 3x^2 + 2By + xy

    (ii) del.(del.F) = 6x + 2B // Differentiating (i)
    \nabla(\nabla.{\b{F}})=\left[\frac{\partial}{\partial x}(\nabla.{\b{F}}),\ \frac{\partial}{\partial y}(\nabla.{\b{F}}),\ \frac{\partial}{\partial z}(\nabla.{\b{F}})<br />
\right]<br />

    (gradient of divergence of F) is a vector.

    RonL
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