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
T′(t) ≠ 0
there is a number τ(t) such that
B′(t)=τ(t)N(t)
where
N(t),B′(t),τ(t)
are the normal vector, binormal vector, and torsion, respetively. Show that the magnitude of the derivative of the binormal vector,∣∣B′∣∣, is equal to the absolute value of the torsion and that a positive value of torsion corresponds to the curve twisting toward N. I am not sure where to begin on this one, so any pointers to help me get started would be really appreciated.
T′(t) ≠ 0
there is a number τ(t) such that
B′(t)=τ(t)N(t)
where
N(t),B′(t),τ(t)
are the normal vector, binormal vector, and torsion, respetively. Show that the magnitude of the derivative of the binormal vector,∣∣B′∣∣, is equal to the absolute value of the torsion and that a positive value of torsion corresponds to the curve twisting toward N. I am not sure where to begin on this one, so any pointers to help me get started would be really appreciated.