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