Hello, i really need help with these

ID: A Name: 12. If a = [1, 2, 3] and b = [3, 2, 1], find a . b. [3, 4, 3] 36 b. 0 d. 10 13. If a = [5, 4, 3] and b = [-2, 3, k], find k such that a and b are orthogonal. a. -1 b. 3 d. 14. If a = [5, -3, 2] and b = [-5, 3, -2], find the angle between a and b. a. 180 C . 90 b. 60 15. Given the points A(1, 2, 3), B(5, 4, 3), and C(2, 1, 2), find AB a. 20 18 b. 20 d. 270 16. Given the points A(1, 0, 0), B(0, 1, 0), and C(0, 0, 1), find projAc AB a. 0 b. d. 17. A father pulls a child in a sleigh with a 150 N force at an angle of 25 to the ground. How much work is done over 2 m ? a. 126.78 J C. 271.89 J b. 126 785.48 J d. 271 892 J 18. A parallelogram is formed by the vectors [-5, 1, 3] and [-2, 3, -4]. Find the area of the parallelogram. a. 1014 square units -2 square units b. C. 25 square units d. 31.84 square units 19. Determine the volume of the parallelepiped formed by the vectors [2, 1, 3], [-5, 1, 0], and [4, 0, -1]. a. 283 cubic units 16.82 cubic units b. C. 19 cubic units d. -16.82 cubic units 2