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Math Help - Vector Fields

  1. #1
    Member iPod's Avatar
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    Vector Fields

    I have attached the question.

    I'm not too sure how to sure that the vector field would be orthogal to the graph of f when f is constant mathematically -how ever I do know the vector field points towards the direction of maximal increase, can this explain orthogonality?

    Also, how can I indicate a maximum or a minimum on a gradient vector field?

    Thank you,
    Attached Thumbnails Attached Thumbnails Vector Fields-vector-fields.png  
    Last edited by iPod; May 14th 2012 at 02:41 PM.
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  2. #2
    MHF Contributor

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    Re: Vector Fields

    I don't understand what you mean by "f is constant". If y= f(x)= C, the graph is a horizontal line in the xy-plane and vectors normal to it are of the form <0, a> for any number, a. If z= f(x,y)= C, the graph is a plane parallel to the xy-plane and vectors normal to it are of the form <0, 0, a> for any number, a.

    vectors do not form a linearly ordered set. It makes no sense to talk about maximum or minimum vectors. You can talk about maximum or minimum length of a set of vectors. is that what you meant?
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  3. #3
    Member iPod's Avatar
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    Re: Vector Fields

    I do apologise, I have now attached the question.
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