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Thread: scalar/vector field question

  1. #1
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    scalar/vector field question

    hey guys, i've been asked to consider the scalar field:

    f(x,y,z) = xy + xz + yz

    after finding grad f, i am asked to find the directional derivative of f at the point P (1,1,1) along the vector field u = [2,-1,1].

    the bit that has confused me is finding the directional derivative of f along the vector FIELD u... do i just calculate the dot product of grad f and the unit vector of u?
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  2. #2
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    Quote Originally Posted by ben08 View Post
    hey guys, i've been asked to consider the scalar field:

    f(x,y,z) = xy + xz + yz

    after finding grad f, i am asked to find the directional derivative of f at the point P (1,1,1) along the vector field u = [2,-1,1].

    the bit that has confused me is finding the directional derivative of f along the vector FIELD u... do i just calculate the dot product of grad f and the unit vector of u?
    Yes. I agree that it sounds a bit odd to use the word field here. I suppose the idea is that it is a constant vector field, taking the value [2,-1,1] at every point (including in particular the point (1,1,1)).
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  3. #3
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    Quote Originally Posted by ben08 View Post
    hey guys, i've been asked to consider the scalar field:

    f(x,y,z) = xy + xz + yz

    after finding grad f, i am asked to find the directional derivative of f at the point P (1,1,1) along the vector field u = [2,-1,1].

    the bit that has confused me is finding the directional derivative of f along the vector FIELD u... do i just calculate the dot product of grad f and the unit vector of u?
    Yes.

    RonL
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