Why is force a vector quantity?

Because if I pull my end of the rope this way and you pull your end of it

that way, the rope doesn't move ... just as if nobody was pulling on it at all.

So the direction of the force must have something to do with the effect it has.

Similarly, when several people are pushing a car to make it move, everybody

knows that they should all push in the same direction. If half of them push on

the back of the car and the other half push on the front, then the people who

understand vectors get very angry.