1. Determine the value of k such that the vectors (3, 5, -1) and (k, 8, 2k -1) are perpendicular. 2. A force of magnitude 5N acts on an object. A second force of magnitude 7N acts at 50 degrees to the other force. What is the magnitude of the resultant of these two forces? 3. A 50N force is applied to the end of a 20cm wrench and makes an angle of 30 degree with the handle of the wrench. What is the torque on a bolt at the end of the wrench? 4. How much work is being done by gravity in causing a 294N rock to tumble 40m down slope at an angle of 52degrees from the vertical? 5. To the nearest degree, what is the angle between the two vectors (1, 2, 0) and (-3, 2, 1)? 6. If ABC is a triangle with vertices A(0, 1), B(2, 0), and C(3, 3), then what is the vector projection of AB onto AC? 7. A parallelogram is formed by the vectors = (1, 0, -1) and = (2, 1, 1). What is the area of the parallelogram? 8. If vector a = (3, 4, 5) and vector b = (8, 7, 6), then what is vector a x b? 9. If lal = 10, |b| = 18 and |a + b| = 23, find la - b| 10. Determine a unit vector that is perpendicular to both a = (3, -4, 5) and b = (2, 1, -3). 11. An object with a weight of 100 N is suspended by two lengths of rope from the ceiling. The angles that both lengths make with the ceiling are the same. The tension in each length is 50 N. Determine the angle that the lengths of ropes make with the ceiling