A billy cart rides down the side of a hill of elevation z = e--2. The cart's path in the xy-plane is given by x(t) = t. from time t = 0 to t = 1. (a) Find the parametric curve r(t) = (x(t), y(t), z(t)) of the cart in the xyz-space. (b) Show that the velocity vector v(1) of the cart for t [0, 1] is 1 21 y(t) = 1 - (-12 v(t): . - (21 +81)e-1-2) (c) Suppose the force of the wind at point (x, y, z) is F = - (*) 0 Calculate the work of the wind force on the cart along its ride for t = [0, 1]. (If the work is positive, then wind helped the cart go faster. If the work is negative, then it made it go slower.) Hint: Recall that W = ds F. The result mentioned in Part (b) may be useful.