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Math Help - Real Analyis, vector valued function,differentiability?

  1. #1
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    Real Analyis, vector valued function,differentiability?

    please help with detailed steps.
    thank a lot~
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  2. #2
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    Re: Real Analyis, vector valued function,differentiability?

    Hey cyhui.

    This reminds of frenet frame considering of a normal vector, a bi-normal and a tangent vector and these things are discussed in curved geometries. Take a look at this:

    Frenet

    You'll notice that there are expressions for Tangent, Normal, and Bi-Normal vectors and all you have to show is that the Tangent vector is non-zero. You have a non-zero normal vector which means that the Bi-Normal and Tangent Vectors are also non-zero.
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  3. #3
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    Re: Real Analyis, vector valued function,differentiability?

    Sorry, i get confused about it. I haven't learn this before.
    Still don't understand how to find the function out.
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  4. #4
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    Re: Real Analyis, vector valued function,differentiability?

    The T in wikipedia relates to <x'(0),y'(0),x'(0)> and the normal vector is non-zero (this is the N) which in this case is (a,b,c) and from the Wiki-page we know that T = F'(x)/||F'(x)|| (which is what the grad refers to).

    Since the normal vector N which is computed from N = T X B is non-zero, the only way this can happen is if B and T are non-zero and also not linearly dependent on each other. So this means that your gradF is non-zero for this reason.
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