(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If c is given in terms of some other parameter t and c'(t) is never zero, show that

k = ||c'(t) x c"(t)||/||c'(t)||^{3}

The first two parts of this problem involved a path parametrized by arc length, but this part says nothing about that, so I assume that this path is not parametrized by arc length.

2. Relevant equations

I have found that

T'(t) = c"(t) = [||c'(t)||^{2}c"(t) - c'(t)(c'(t) dot c"(t))]/||c'(t)||^{3}

I am having trouble figuring out how to relate the curvature to the equation

k = ||c'(t) x c"(t)||/||c'(t)||^{3}

3. The attempt at a solution

I can express the equation as the components so

F(x,y,z) = [(z"y'-y"z')^{2}+(x"z'-x'z")^{2}(y"x'-x'y")^{2}]^{1/2}/(x'^{2}+y'^{2}+z'^{2})^{3/2}

Where should I go from here, and is the above equation useful at all? Do I need to find

||c"(t)|| as well (and is that even possible)?

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# Homework Help: Curvature Proof Problem

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