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Math Help - Vector Algebra

  1. #1
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    Vector Algebra

    Given

    V (x , y , z) = 10xyz - (x^2)z + 10y(z^2) -20

    find the grad of V.

    if i transfer to the form below the how do i associate the -20 with ?

    10xyz ax - (x^2)z ay + 10y(z^2) az -20


    anyone able to help?
    is the answer 10yz - 0 + 20yz ?

    many thanks
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  2. #2
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    Please explain how you got this form '10xyz ax - (x^2)z ay + 10y(z^2) az -20'?
    and how you get 10yz +20yz


    If you are trying to get the gradient of V(x,y,z) you will need to express the gradient in the direction of x, the direction of y and the direction of z.

    Thus you should be looking at how you might express this gradient as a vector with partial derivatives.
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  3. #3
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    Quote Originally Posted by Chris0724 View Post
    Given

    V (x , y , z) = 10xyz - (x^2)z + 10y(z^2) -20

    find the grad of V.

    if i transfer to the form below the how do i associate the -20 with ?

    10xyz ax - (x^2)z ay + 10y(z^2) az -20


    anyone able to help?
    is the answer 10yz - 0 + 20yz ?

    many thanks
    The derivative of a constant is 0.

    However, your whole concept here is wrong. The grad of a function is a vector:
    \nabla f(x,y,z)= \frac{\partial f}{\partial x}\vec{i}+ \frac{\partial f}{\partial y}\vec{j}+ \frac{\partial f}{\partial z}\vec{k}
    not another real valued function as you have written it.
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