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Let $r(t) = e^t \cos(t)\ \hat{i} + e^t\sin(t)\ \hat{j} + e^t\ \hat{k}$ be a vector valued function.

Interpret $r$ as the position of a moving object at time $t$: find the curvature of $r$ at time $t$, and determine the tangential and normal components of acceleration.

Any help AT ALL?

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    A problem with this question is that it's phrased as if the poster is passing on to us verbatim an exercise written by someone other than the poster, instead of asking his own question about that exercise.2012-08-28

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Hint: use this formula to find the curvature:

$ \kappa(t) = \frac{\lvert r'(t)\times r''(t) \lvert}{\lvert r'(t)\lvert^3}. $

For the other two things, try to take a look here.

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    @Nick: Yes, the symbol on the left is a kappa that is often used for curvature. Try and take a look at the link that I provided so see how you can find the other things.2012-08-28