Compute each part of given problem:
Problem: A skier travels first 2 miles in the direction north, 3 miles in the direction west, and finally 1.5 miles in the direction south. In which direction should the skier go to the return along the shortest path to get back to his original position?
Part A: Draw an accurate sketch, showing all the vectors of the skiers' movement.
Part B: Draw a vector of displacement that would take the skier from its final to its initial position. How is this vector related to the above vectors of skiers' movement?
Part C: Determine the direction of the above vector from part b.
Show your reasoning and calculations for above problem.