## Finding the unit tagent vector, normal vec and curvature problem

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.
http://show.imagehosting.us/show/800..._-1_800636.jpg
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 Recognitions: Gold Member Science Advisor Staff Emeritus In finding N, you did NOT find T'/|T'|. You used r' rather than T. Yes, $$T= /\sqrt{t^4+ t^2+ 1}$$. To find N(t) you have to differentiate THAT: differentiate $$\left<\frac{t^2}{\sqrt{t^4+ t^2+ 1}},\frac{t}{\sqrt{t^4+ t^2+ 1}},\frac{1}{\sqrt{t^4+ t^2+ 1}}\right>$$.

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