Calculus Help

1. A bee flits from flower to flower. If it leaves the hive and travels 220 m [N32*E] and then 35 m [S48 W], how far and in what direction is the bee from its hive? 2. A 70-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 [$5'E] of Barrie. If the wind is blowing from the South with a velocity of 45 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 . bta . c b.a *( 6+c)= axbta *c ca * ( b . c)= axb.a * c 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 25 N, what are the tensions in the two wires as shown below? 56 45 25 Newtons