Answer
$221^{\circ}$ which is south west
Work Step by Step
We have three vectors representing the three parts of the path:
$\vec{a} = 3.1\,km\, \hat{i}$
$\vec{b} = -2.4\,km\, \hat{j}$
$\vec{c} = -5.2\,km\, \hat{i}$
Add these up to get the total displacement:
$\vec{t} = -2.1\,km\,\hat{i} - 2.4\,km\,\hat{j}$
The angle of the displacement is:
$tan^{-1}(\frac{-2.1\,km}{-2.4\,km}) = 41^{\circ}$
Because both the x and y components are negative, we must add $180^{\circ}$ to get the correct answer (remember $tan^{-1}$ is restricted to between $-90^{\circ}$ and $90^{\circ}$): $221^{\circ}$
$221^{\circ}$ is southwest.
