Test 6. Cartesian Vectors 1. Given the vectors a = (-3, 2, -1) and b = (2,4,-3). Determine the following. a. a . b. (2 marks, K) b. a x b. (3 marks, K) C. The angle between a and b. (2 marks, A) d. The area of the parallelogram formed by the vectors a and b. Show all steps. (2/2 marks, A/C) e. The vector projection of a on b. (2 marks, K) 2. Given the vectors a = 41 + 2j - k and b = 31 - 27 + 5k. Determine the following. a. a . b. (2 marks, K) b. a x b. (3 marks, K) c. The angle between a and the x axis. (2 marks, A) d. a . (2a - 3b) + 4b . (4a + 2b). Show all steps. (2/2 marks, A/C) 3. Given the points A (2,3,7), B (3, 6,5) and C (-1,2, -2). a. Is triangle ABC a right triangle? Explain your solution. b. Determine the area of the triangle ABC. Show all steps. (6/4 marks, T/C)