Deep sea diver vectors problem

Question

A deep sea diver swan 30 m due east then 120 m deep down and finally 40 m due south to reach a wrecked ship. How far is the wrecked ship from the diver's starting point ? (Solve using vectors)

Answer 1

The 3 swim distances are mutually perpendicular, and therefore can be treated as the components of a displacement vector in Cartesian coordinates.  Then the net distance is the magnitude of the displacement vector:

 

d = (30i - 120j + 40k) m

 

d = sqrt[(30)^2 + (-120)^2 + (40)^2] m = 130 m