(1) For the curve r(t) = e costi + e sintj + tk find the unit tangent vector T(t) and parametric equation of the line tangent to the curve at the point P(1, 0, 0). (2) Find T(t), N(t), aT and an for the curve r(t) = elite j + tk for t = 0. (3) A particle moves along the path given by r(t) = (t - sint, 1 - cost), t 2 0. (a) Let C be the curve represented by r(t). Find all t 2 0 for which C is not smooth. (b) Find aT and an at t = 1/2, 1, 37 /2. (c) Determine whether the speed of the particle is increasing or decreasing at each of the above mentioned values of t. (d) Find the distance (arc length of the path) traveled by the particle from t = 0 to t = 27