Problem 9. The vector function r(t) = (cost + tsin t)i + (sin t − t cost)j + 1 2 √ 3t 2k determines a curve C in space. (a) Find the unit tangent vector T(t) and the principal normal vector N. (b) Find the curvature, κ of C. (c) Determine the tangential and normal components of acceleration; express the acceleration vector, a(t) in terms of T and N.