1.6.3 The Binormal Vector
So far we have associated two unit vectors with parameterized curves - the unit tangent and the unit normal. There is a third vector known as the binormal defined as the cross product of the unit tangent and the unit normal:
To define the unit tangent and unit normal it was required we divide by a length to achieve a unit vector. However in my definition of the binormal there is no such requirement. Explain why the binormal vector must always be a unit vector.
is perpendicular to both and . We can think of the vectors as forming a mini-basis for where we've re-centered the origin to be the point along the curve. Together these three vectors are called the Frenet Frame.