. Find scalar c > 0 such that the magnitude of 4i + cj + 12k is 13. . A bird ies due east at 24 mph while experiencing an 8 mph wind blowing 30 north of east and a 5 mph updraft. What is the bird's groundspeed in mph, which is the speed as observed from the ground? . Find t such that (21? 1, 5 1?, 2t) is orthogonal to (-2, 1,2). . For the following vectors u and v, express u as the sum 11 = p + n where p is parallel to v and n is orthogonal to v: (a) u = (3,4), v = (1,1) (b) u = (2,2,7), v = (1,1,2) . Find the area of the parallelogram with vertices at (1,2), (4, 6), (9, 7) and (6, 3). . Find a vector-valued function whose graph traces out the line through the points (1, 2, 3) and (4, 5, 6) and the distance from this line to the origin. . Find a vector-valued function for the tangent line to the curve C that is the graph of v(t) = (t In (t), 2 t2, cos (711)) at the point (0, 1, 1)