Proving the Relationship between Velocity and Curvature in a Vector Equation

[Baumer8993]

Homework Statement

This is part of the proof for curvature.

Prove V X A = k(ds/dt)³B

B is the the binormal vector. I have seen something in the proof with a T X N which I know is B.

Homework Equations

I have already proven

a(t) = (d²s/dt²)T + K(ds/dt)²N

The Attempt at a Solution

I have seen some things where you start with v(t), and take the derivative then take a cross product, but I am not sure if this is how my professor wants us to do it. He wants us to use the a(t) part from above to prove it.

 

[tiny-tim]

Hi Baumer8993!

Isn't V = (ds/dt)T ?