. Triangle ABC has vertices A(4, 7, 7), 8(1, 6, 5), and Cl2, 9, 8). Which kind of triangle is AABC? Justify your answer. (4 marks) . The points (-2, 4, 5), (4, 5, 3), and (1, -1, 6) are three of four vertices of parallelogram ABCD. Explain why there are three possibilities for the location of the fourth vertex and nd the three points. (4 marks) . The points A(2, -1, z), B(2, 4, 3), and C(10, y, -1) are collinear. Find the values of y and z. (2 marks) . Explain the meaning of direction angles and their relation to direction vectors. (6 marks) a. What are the direction angles of the vector [5, 1, 8]? _\\ b. If a point P lies on the :c-axis, what are the direction angles of the position vector OP? c. Prove that cos2 (a) + cos:2 ([3) + cos2 (7) = 1. d. Avector has direction angles a = 85 and B = 65 a. Find the value of 'y. b. Find a vector that has those direction angles. e. Explain why it is not possible for two of a vector's direction angles to be less than 45. f. What is the value of sin2 (a) + sin2 () + sin2 ('y) ? Why