The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t2). (a) Find the speed of the particle at time t0 = 4π. (b) Is c'(t) ever orthogonal to c(t)? Yes, when t is a multiple of π. Yes, when t = 0. No (c) Find a parametrization for the tangent line to c(t) at t0 = 4π. (Enter your answer as a comma-separated list of equations in (x, y, z) coordinates.) (d) Where will this line intersect the xy-plane?