PART C: THINKING 6. Determine if the vectors a = [-1,5, 3], b = [-2, 4, 7], and c = [10, 7, 1] are coplanar. 141 7. Given a = [4, 7, 1] and b = [-3,1, 5]: a) Calculate the angle between a and b. 131 b) If c = [3, -4, t], find t so that a and c are perpendicular. (31 Page 8 of 1313. A force, F = [12, 15, 47] N is applied over a distance of d = [125, 85, 147]m. Determine the amount of work, measured in Joules, done in this situation. 131 14. Find the magnitude of the torque vector, measured in Newton-meters, produced by a cyclist exerting a force of F = [60, 15, 105]N on the shaft-petal i = [10, 13, 50]cm long. Recall: 7 = F X F8. Calculate the area of the parallelogram whose adjacent sides are: a = [6, 3, -2] and b = [1, 3, -1] 14 9. The points A [-1, 1, 1], B [2, 0, 3], and C[3, 3, -4]. Show that this triangle is a right-angle triangle. 13] 10. Determine the following: a) Determine the vector equation of the plane that contains the following two lines L1:r = (2,3, -5) + t(3, 1, 5), tER [21 L2:1 = (2, 3, -5) + s(0, 4, -3), SER b) Determine the corresponding Cartesian equation. 151 Page 9 of 13