5. (10 pts) A hiker observes that when she walks in the direction i, the temperature decreases at 0.50 per km. When she walks in the j direction, the temperature increases by 20 per km. When she walks in the k direction, the temperature decreases by 10 per km. (a) (5 pts) What direction should the hiker walk if she wants to warm up as fast as possible? (b) (5 pts) At what rate will the temperature change when she walks in the direction