The idea of a vector. Adding and subtracting vectors

Quantities such as length, area and mass are determined by a number alone and are called scalar quantities. To know a quantity like force or velocity completely we also need its direction; these are called vector quantities. In geometry a vector is pictured as a segment with a direction: in →AB, A is the beginning, B is the end, and the length is the modulus |→AB|. A vector whose beginning and end coincide is the zero vector, and its modulus is 0. Vectors lying on one line or on parallel lines are collinear; they are codirectional if they point the same way and oppositely directed if they point opposite ways. Vectors with equal modulus and the same direction are equal, and a vector may be moved to any point without changing its modulus or direction.