Expert: Abe Mantell - 6/7/2011

Question
What is the derivative of Unit Binormal in terms of r(t)>

Unit Binormal= r'(t) x r''(t) / ||r'(t) x r''(t) ||

Answer
Hello Roger,

Since the derivative of a cross-product follows the usual "product rule"
and ||r'(t) x r''(t)|| is just a scalar, we get the derivative is:
{[r'(t)]' x r''(t) + r'(t) x [r''(t)]'}/||r'(t) x r''(t)||
= {r''(t) x r''(t) +  r'(t) x r'''(t)}/||r'(t) x r''(t)||, but v x v = 0 (i.e. the zero vector)
= {0 + r'(t) x r'''(t)}/||r'(t) x r''(t)||
= r'(t) x r'''(t)/||r'(t) x r''(t)||

OK?

Abe