Why is the location/direction of a vector important in analysis?

The direction of a vector is important because some directions are positive and some are negatvie so when you go and do calculations with the numbers you need to make sure you are you the right signs that are known with each direction. For example, if the direction of the vector is south, the value of that vector should be negative while if you go north then the value is positive. If you don't get these signs right then your answer will be very different from the correct answer.