1. (20 pts) Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. a) The curve with vector equation r(t) = t3 i + 2t3 j + 3t3 k is a line. b) If k(t) = 0 for all t, the curve is a straight line. c) If u(t) and v(t) are differentiable vector functions, then d [u(1) X v(1)] = u'(t) X v'(t) d) If |r(t) | = 1 for all t, then r'(t) is orthogonal to r(t) for all t