Add and Subtract by Components

A vector is a quantity that has both a magnitude and a direction. An example is a force f. In contrast, a scalar quantity, such as work, is a single number. Vectors are represented as arrows having a length, which represents the magnitude, and a direction. Vectors are indicated by bold type, such as x and v. 

Mov ing the origin does not change the magnitude or direction of a vector, so vectors can be added, vi -i- = V2 + vi = v, by placing them head to tail as 

The magnitude and direction of a vector do not depend on what the coordinate system is, but the components do. To dehne the Cartesian coordinate system, for example, let i be a vector that is directed along the x-axis, and 

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