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Finding the unit tagent vector, normal vec and curvature problem

  1. Oct 14, 2005 #1
    Hello everyone, the problem says to:
    For the curve gien by r(t) = <1/3* t^3, 1/2 * t^2, t>
    find (a) The unit tagent vector;
    (b) the unit normal vector;
    (c) the curvature;

    Well it seems easy enough! the formula's are just derivatives for instance:
    The unit tagent vector says:
    T(t) = r'(t)/|r'(t)| i got this one right, you can see my work on the image below:
    but part (b) i missed..
    The normal vector N is suppose to just be:
    N(t) = T'(t)/|T'(t)|;
    Here is my work and it does not match the back of the book.
  2. jcsd
  3. Oct 14, 2005 #2


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    Staff Emeritus
    Science Advisor

    In finding N, you did NOT find T'/|T'|. You used r' rather than T.

    Yes, [tex]T= <t^2, t, 1>/\sqrt{t^4+ t^2+ 1}[/tex].
    To find N(t) you have to differentiate THAT: differentiate
    [tex]\left<\frac{t^2}{\sqrt{t^4+ t^2+ 1}},\frac{t}{\sqrt{t^4+ t^2+ 1}},\frac{1}{\sqrt{t^4+ t^2+ 1}}\right>[/tex].
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