>>2
As this guy said. Also, we can then apply properties and basis to the vector space. Most people are generally familiar with vectors in normal euclidean vector space of the basis (1,0) and (0,1) which they then apply properties (for applications) like centimeters for distance, or centimeters per second for velocity, and many others (eg, a car is has a acceleration vector pointed in the direction it's tires are facing which is measured in the units meters per second per second (m/s^2).