Determine whether each of the following is true or false. (a) Any two distinct non-parallel lines in R must have an inter- section point. (b) Let f,g: R R be two smooth functions. Define the smooth function h: R2 R by h(x, y) = f(x)g(y). If P(x) and Q (y) are the first-order Taylor's polynomials of f(x) and g(y) using 0 as the reference point respectively, then the second-order Taylor's polynomial of h(x, y) using (0,0) as the reference point must be P(x)Q(y). (c) Define F: R R by F(x, y, z) = (z + sin x, y cos x, yz). Then F is not the curl of any vector field in R of class C. (d) Let C be the line segment in R2 joining the points (0,0) and (1,1). Then there are exactly two different parametrizations of C.