Ahmed, Brett and Camille decide to go skiing at Bromont, a mountain an hour east of Montreal by car. The ski hill is described by the graph of z=e 22_3y2 +12y-12 with z representing elevation. The chair lift brings them close to the summit, placing them at coordinates (1, y) = (1,2). a) Ahmed is a thrill-seeker and wants to go downhill in the steepest possible direction. Determine which direction he should go. Your answer should be a unit vector. b) Brett is afraid of skiing and wishes he had stayed home. To pass the time, he would like to walk along a path of constant elevation. Determine one of two (unit vector) directions he can start walking to achieve this goal. C) Camille is an excellent skier, but is in no hurry to get to the bottom of the mountain. She would like her initial direction to be half as steep as Ahmed's. Show that the ideal direction (u, v) for Camille to travel will satisfy the equations 1=2u, 1=u? + v?, but do not need solve these equations. Ahmed, Brett and Camille decide to go skiing at Bromont, a mountain an hour east of Montreal by car. The ski hill is described by the graph of z=e 22_3y2 +12y-12 with z representing elevation. The chair lift brings them close to the summit, placing them at coordinates (1, y) = (1,2). a) Ahmed is a thrill-seeker and wants to go downhill in the steepest possible direction. Determine which direction he should go. Your answer should be a unit vector. b) Brett is afraid of skiing and wishes he had stayed home. To pass the time, he would like to walk along a path of constant elevation. Determine one of two (unit vector) directions he can start walking to achieve this goal. C) Camille is an excellent skier, but is in no hurry to get to the bottom of the mountain. She would like her initial direction to be half as steep as Ahmed's. Show that the ideal direction (u, v) for Camille to travel will satisfy the equations 1=2u, 1=u? + v?, but do not need solve these equations