18. Show that the vectors (-1, 2, 6), (3, 2, -1) and (7, 10, 9) lie on the same plane. 19. The vertices of quadrilateral ABCD are given as A(0, 3, 5), B(3, -1, 17), C(4, 1, 3) and D(7, -3, 15). Prove that ABCD is a parallelogram.20. A sign is hanging from a storefront. The two ropes holding it are fixed at angles of 250 and 350 with the horizontal. If the sign has a weight of 1150 N, what is the tension in each rope? 21. A plane needs to travel to a location 1550 km away, at a direction [N30 E]. The plane flies at a velocity of 625 km/hr, and there is a wind of 80 km/hr at a direction [N10'w]. a. What heading should the pilot take to arrive at the destination? b. How long will it take? 22. Find the area of the triangle defined by the following three points: A(2, 4, 5), B(5, 0, 6) and C(1, -3, 4).23. Find the vector, parametric and symmetric equations of the line which contains the point (5, - 3, 8} and is perpendicular to the plane 3):: + By II": + 3 = D. 24. For the points {2, 5, 1}, (D, 4, and {1, 5, 9}, a. Find the vector equation of the plane containing these points. in. Find the Cartesian equation of the same plane. c. Does the point {1, 5, 2} lie on this plane? 25. For the plane 2x - 3y + z -8 =0, a. Find the equation of a line which is perpendicular to the plane. b. Find the equation of a line contained within the plane