QUESTION 1 Note: For any vector v = (1,4, 2) R, we call whor = (1, y,0) the horizontal component of the vector v. (i) In this question we consider the path h : [0,6] : R+R:t(cos(t), sin(t), t). (a) Roughly draw the curve corresponding to h. (b) Compute the length of h. (c) Compute the angle (t) between h' (t) and the horizontal component of h'(t), for t (0,6m). (ii) Consider now the path 9 : [0,6x) : R+R: (cos(t), sin(t),t + f(t)), with f: R+R a differentiable function such that f(t) > 0 and f'(t) > 0. (a) Give an expression of the length of g. (b) Show that the length of g is greater than the length of h. (c) Give an expression of the angle a(t) between g'(t) and the horizontal component of '(t). (d) For t (0,67], do you expect to have a(t) > 0(t) or a(t) 0 and f'(t) > 0. (a) Give an expression of the length of g. (b) Show that the length of g is greater than the length of h. (c) Give an expression of the angle a(t) between g'(t) and the horizontal component of '(t). (d) For t (0,67], do you expect to have a(t) > 0(t) or a(t)