\\ I 9.12. Let a be a path in R3 that lies on the sphere of radius a centered at the origin, that is: CH [0 NW)\" = a for all t. Let T(t) be the unit tangent, N(t) the principal normal, 11(t) the speed, and Mt) the curvature. Assume that 11(t) 7E 0 and T'(t) 75 0 for all If so that the Frenet vectors are dened. (a) Show that a(t) - T( 0 (b) Show that n(t)a(t) N(t) : 71 for all t (Hint: Differentiate part (a).) (c) Show that [$05) 2 QIH t for all t. ): for all t. CHAPTER 2. PATHS AND CURVES 63 326