Problem 3: Before you begin this exercise you should remind yourself of the cross product and. its properties {Section 12.4 in the book). 1. Let f : [R l- R3 be a vector valued function (so t E R maps to t) E R3). Let c 73> U be a real constant. Assume that ||f(t)|| = c for all t E R. Prove that g) is orthogonal to t] for all t E R. Hint: Recall that two vectors 3:, p E R3 are orthogonal if their dot product is zero :1: - y = . . Let t } t) for t E [0,1] be a parametric curve in R3. Prove that the curvature satises a s9 lljt} s so)\" at = (j llii-lglll3 . Let t :~ r(t) = (t), y(t)) for t E [U1 1] he a parametric curve in R2. Prove that seatat) sense) i ( (so): + (emf) You can use part 2. Notice that you can think of a 2D curve in 3D Irv setting the last coordinate equal to [1; t > {so}, mam. a(t} =