The plane determined by the unit normal and binormal vectors N and B at a point P on a curve C is called the normal plane of C at P, and the plane determined by the unit vectors T and N is called the osculating plane of C at P. Consider the curve C described by the position vector r(t)=t³ i+3t j+t⁴k.
(a) What are the coordinates of the center of the osculating circle to the curve C at time?
(b) What is the standard equation of the osculating plane for path C at time t?
