The nice part of the problem is that it states that the rain outside of your apartment is straight down. So, this vector only has a y component. From the problem, it is probably OK to assume that L is driving on a flat highway. So, the vector from the car motion only has an x component. Be sure to get velocity from the car and apartment in the same units. You just have one x and one y. Add these vectors with the Pythagorean theorem to get the magnitude. The resultant direction of the vector would be the arctan(y/x). Remember signs for the arctan. The direction will be almost horizontal, but slightly downward by the angle you calculated.
