How do I answer these questions? (#6 - 15)

6. Express the longest vector in each diagram as the sum or difference of the other two vectors. [T - 3) 3. b. 7. ABCDEF is a regular hexagon, with centre at 0. Let Ali = # and BC = y. Express each vector in terms of a and ). (sum/difference) (A -5) a. ED b. CD c. CF d. Of e. FD 8. The diagram shows a parallelepiped. Determine a single vector (with head and tail on the parallelepiped] that is equivalent to each sum or difference. (T - 6) a. AR - BF b. AB + CG c. EF + DH d. AB + HD + FG e. AB -HD +FG F. ED + AB - (HG + FB) 9. A, B. C. D. E, and F are any points on the same plane. Write a single vector equivalent to each expression. Be sure to show your work. (A -6) a. AR + BC + CF b. BA + CE - CA c. DF - DC - CE 10. An airplane is flying with airspeed 400 km/h on a heading of 000". There is a 50 km/h wind blowing from the direction 090". a. Draw a vector diagram to illustrate the situation. (C-2) b. Calculate the ground velocity of the plane. (T - 2]11. A swimmer, who can swim 3.5 m/s in a pool, heads directly across a river with a 2.0 m/s current. a. Draw a vector diagram to illustrate the situation. (C-2) b. Calculate the swimmer's actual bearing and speed relative to the shore. (T -3) 12. A sign weighing 400 N is hanging from two ropes. One rope is attached to the ceiling and makes an angle of 40" with the ceiling. The other rope is attached to the wall, and makes an angle of 50" with the wall. Determine the tensions in the ropes. Be sure to include a diagram. (C- 3, A-3) 13. A pilot flies on a heading of /40'W with an airspeed of 240 km/h. Her actual ground velocity is 250 km/h at a bearing of N42"W. a. Draw a vector diagram to show the air velocity, ground velocity, and wind. (C - 3] b. Calculate the speed and direction of the wind. (A -5) 14. An airplane taking off moves at 500 km/h at an angle of 4 to the horizontal in the direction W30N for 10 min. Calculate its final altitude and horizontal displacement from the airport. (A-4) 15. In a collision, the total momentum (the combined momentum of all objects) is unchanged. A curling stone is moving straight down the ice at 3.5 m/s when it collides with a stationary stone of equal mass. After the collision, the struck stone is moving with a velocity of 2.0 m/'s in a direction 30% to the right of "straight down the ice". Use components to calculate the velocity (magnitude and direction) of the original stone immediately after the collision, to 2 decimal places, and the direction with respect to "straight down the ice". Include a diagram for full marks. (C-3, A -5)