1. Suppose that r(t) = (3 cos(2t) - t, 3 sin(2t), 2t). a. Determine the velocity, the acceleration and the speed for t = /2. b. Determine whether the angle between the velocity vector and the acceleration vector for t = /2 is right, acute or obtuse. c. Find the vector equation of the tangent to the trajectory of r for t = /2. 2. Suppose that a motion described by the vector valued function (i.e. position function) r(t) has velocity given by r'(t) = v(t) = (3 cos t, 3 sint, -1) and that r(0) = (3, 1, 1). Find the formula for the position function r(t). 3. Find the length of the trajectory of the vector valued function f(t) = (52-t, est, e-5t) from 0 to In 2 and express your answer in the form a/b where a and b are natural numbers.