17. Find any possible solutions for the 3 planes below and explain geometrically what situation the planes are in. 10. Determine the parametric equation of the plane that contains the line +2_ _ 2-2 and the point State any possible points/ lines of intersection. [6 marks] P (2, 5, 3) 4x - 2y + 2z = 2 a. x = 2+5s + 3t, y = 5+ 3s + 2t, z = 4+ 2s +1, s,te R 3x - 5y + 42 = 3 b. x = 5+ 25+ 2t, y = 3- 3s + 5t, z = 2- 2s + 31, s,te R c. x= -2+ 5s + 21, y = 3+ 3s + 5t, z = 2+ 25 + 3t, s,te R 3x + 2y - 1z = 0 d. x = 2+ 5s +4t, y = 5+ 3s + 2t, z = 3+2s+1, s,te R 11. The prism on the right is bisected by the xy-plane. The point P = (3, 7, 3). Determine C a. (0, 7, -3) C. (0, -7, -3) b. (0, 7, 3) d. (0, -7, 3) 12. An airplane is heading north with an airspeed of 400 km/h. The plane encounters a wind from the east at 100 km/h. What is the magnitude of the resultant ground velocity? 400 km/h c. 500 km/h b. 387 km/h d. 412 km/h 13. The two planes 3x- 2y -42 + 1 = 0 and 2x - 5y - 3 = 0 are: a. perpendicular parallel and distinct b. coincident d. none of the above 14. In the diagram on the right, vector C represents: a. B- A + C b. to ! : d. D+B 18. Determine the point of intersection of the plane with vector equation r = (5,3,-2) + s(1, 3,2) + :(2,4, 0), 15. Which of the following equations is a plane parallel but not coincident to the plane x - 3y + 2z = 4? s, # E R, and the y-axis. [3 marks] a. x - 3y + 32 = 4 C. 3x - 9y+ 62 = 12 b. none d. 2x - 6y + 4z = 4 16. Determine the vector projection of RS on RT. [4 marks] S(1, 5) T(3, 1) 19. Calculate the area of the parallelogram formed by the vectors a = (3,2, -2) and b = (2, -1,2) [3 marks] R(-4,-1)