Applications of Vectors 1. Determine the angle between the vectors a" = (8,3,5) and b" = (2,9, 4). 2. How much horizontal work is done if Mrs. Bethany is pulling a trolley on a flat surface for 70 m and she is pulling with a force of 80 N along the handle, which is at an angle of 43" above the horizontal? 3. Determine the normal of the vectors a" = (8,3,5) and b" = (2,9, 4) 4. Determine the magnitude of the torque on a nut if the wrench is 21cm long and if the 50 N force is applied at an angle of70 to the wrench. 5. Find the scalar projection of the vector a" = (3,2,6) on b" = (2,0,8). 6. Determine the vector projection of the vector a\" = (9,2,6) on b" = (3,2,8). 7. At what bearing should a ship aim in order to travel at a bearing of 98" if the 23 km/h wind is pushing the boat at a bearing of 072 and the ship's propellers are pushing it at a speed of 89 km/h? 8. What is an equilibrant? 9. A mass of 90 kg is suspended from a ceiling by two lengths of rope that make angles of 40 and 60" with the ceiling. Determine the tension in each of the ropes