Scalars and Vectors

Scalars vs vectors. A scalar is a quantity that is completely described once you know how much of it there is — its magnitude, and nothing else. Distance, length, speed, temperature, voltage, mass, pressure and work are all scalars: '$5$ kg' or '$40^\circ$C' is a complete description.

A vector is a quantity that needs both a magnitude and a direction to be fully described, and for that reason it is naturally pictured as a directed line segment. Force, displacement, and velocity are vectors: knowing a force is '$10$ N' tells you nothing about which way it pushes. …