The second problem is more complex and requires vectors to take care of the 3 directions involved. The first (car) problem has only one direction so no need for vectors.
The first problem is asking for a moment about an axis. I'm pretty sure this is why you have to employ the unit vector in your calculations. If i recall correctly (been awhile since I was in statics) the unit vector here will be j or [0i 1j 0k]. Is that familiar?
The second problem is asking for a moment about a point.