JUST give the answer and easy process

10. (7 points) [K, T] (a) Given the square-based prism shown, state whether each statement is true or false. i) AB = GH E H G A D ili) AH = BG B (b) Give an expression that is equivalent to each of the following. i) AB + FH + CB ii) HB - DB 11. (7 points) [K] Given vectors a = (-1, 0, 3), 5 = (2,3, 1), and = (1, 3, -3), determine each of the following: (a) 2a + C (b) -b. a (c) 3(a . c) + (b . a)12. (8 points) [A] An airplane is heading south at speed 400 km/h. The airplane encounters a wind from the east blowing at 100km/h. (a) Draw a diagram of the vectors involved in this problem. Be sure to include a compass! (b) How far will the airplane travel in 3 hours? (c) What is the direction of the airplane? 13. (8 points) [K, T, C] (a) Determine the Cartesian equation of the plane that contains the line F = (2,3, 2) + t(1, 1, 4) and the point P(4, -3, 2)14. (10 points) [K, T, C] Determine an equation for a line that has the same x- and z-intercepts as the plane 3x + 4y - 2 = -12. Give your final answer in parametric form. 15. (10 points) [T, C] (a) Prove that the following system of equations has no solution. w1 : 2x + 4y - 2 +12 = 0 72 :-x+2y-72 = 0 73 : 62+ 12y -32 -5 = 0 (b) Draw a sketch of 3 planes that can be used to represent the system of equations above. Hint: You DO NOT need to draw the x-,y-, and z-axes of RS. Just draw the planes.