Torsion of a curve question

kankerfist

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Mar 22, 2006
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I have come across the following question while studying for my calc 3 exam. For each t at which
T(t)\displaystyle \vec T'(t)0\displaystyle \vec 0
there is a number τ(t)\displaystyle \tau (t) such that
B(t)=τ(t)N(t)\displaystyle \vec B'(t) = \tau (t)\vec N(t)
where
N(t),B(t),τ(t)\displaystyle \vec N(t),\vec B'(t),\tau (t)
are the normal vector, binormal vector, and torsion, respetively. Show that the magnitude of the derivative of the binormal vector,B\displaystyle ||\vec B'||, is equal to the absolute value of the torsion and that a positive value of torsion corresponds to the curve twisting toward N\displaystyle \vec N. I am not sure where to begin on this one, so any pointers to help me get started would be really appreciated.
 
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