Problem 1. Let F(x, y) = (y, x). a) Sketch the vector field with at least 15 vectors drawn. b) Suppose at t = 0, a particle is placed a the point (1, 2) in the vector field (one can imagine that the vector field describes the velocity of a fluid). Find the location of the particle r(t) at time t. c) In the same scenario as the previous part, write down an equation in x and y that describes the curve traced out by the particle's motion.