Hello I need help with these vectors question. For a good review please be detailed and thorough with the answers. Thank you :)

1. A bee flits from flower to flower. If it leaves the hive and travels 210 m [N32 E] and then 37 m [S51 W], how far and in what direction is the bee from its hive? 2. A 100-N force is applied to the end of a 50-cm wrench and makes an angle of 45 with the handle of the wrench. a) What is the torque on a bolt at the other end of the wrench? b) What is the maximum torque that can be exerted by a 100-N force on this wrench and how can it be achieved? 3. An air ambulance is travelling from Barrie to Toronto. Toronto is located 90 km [S5 E] of Barrie. If the wind is blowing from the South with a velocity of 62 km/h, and the plane's air speed is 375 km/h, what direction must the pilot fly to make it to Toronto? 4. State whether or not the following statements are true. Justify your reasoning. a. a . (b + c) = a . b+ a . c bax ( b + c ) = axb+axc cax ( b . c ) = axb . axc 5. Find the volume of a parallelepiped with 3 edges defined by a = (-2, 0, 4), b = (5, 9, 0) and ~ = (0, 3, -7). 6. A traffic sign is hanging from two wires. If the weight of the sign is 35 N, what are the tensions in the two wires as shown below? 56 450 35 Newtons 7. A vector can be used to represent the path of a drill tip used to bore a deep mine shaft in Sudbury one quarter of the way to the centre of the Earth. Represent the vector using a directed line segment and Cartesian co-ordinates and describe which representation may be more suitable in this situation. 8. Describe three situations in which you may want to know the projection of one vector onto another