Match each curve in R with its parametrization. . An ellipse lying in the yz-plane . The intersection of the plane y = -x and the plane z = 4 . A line segment starting at (-1, 1, -1) and ending at (1, 0, 1) . A helix lying on the cone a2 + y2 = z2 Drag or tap the options below to fill in the blanks T (t) = (1 + t, 1 - t, 4), te (-0o, 00) T(t) = t(-1, 1, -1) + (1 - t) (1, 0, 1), te [0, 1] T (t) = (3 cost, 0, (sint) /5), te [0, 27] r(t) = (cost, sint, t2), t > 0 r (t) = (0, 5 cost, 3 sint), te [0, 27] T ( t ) = (VE, t, t2 ), + 2 0 T (t) = (t cost, t sint, t), t 2 0 T ( t) = (t, -t, 4), te (-00, 00) T(t) = (1 - t)(-1, 1, -1) + t(1, 0, 1), t c [0, 1] SAVEAttime t = 0 a leaf on a tree has position 7(0) = (0,0, 100). At = 0 a gust of wind loosens the leaf from the branch giving it an initial velocity #'(0) = (0,1000, 2). The leaf enters free-fall and so has acceleration #"(t) = (0, 0, 10). The leafs position is described by the parametric curve 7(t) = . This curve is a D in the Dplane. \fConsider the curve T (t) = (et sint, et, et cost) , - co