This is a question about "Galilean Relativity." (No, not the Einstein stuff. You're safe. ) In Galilean Relativity velocities add. No fuss, no mess.

I find it to be more convenient to solve for b) first. You should be able to easily construct the argument for a) from the same ideas. (It's just the way I think things through.)

b) You are in a car traveling at 90 km/h. This means that the ground is moving by you at 90 km/h. The oncoming car is traveling at 120 km/h with respect to that same ground and moving in the same direction as that ground. Thus the relative speed of the oncoming car to you is 90 km/h + 120 km/h = 210 km/h. The direction is, of course, directly away from you.

a) This is just the opposite of the above. So the speed of you with respect to the other car is also 210 km/h. The answer for the velocities of part b and part a are in opposite directions, but have the same magnitude. So the direction is directly toward you in this case.

-Dan