Unit Vector Notation

When we want to specify a vector by its components, it can be cumbersome to have to write the algebra symbol for each component:

A more compact notation is to write

where the vectors

, called the unit vectors, are defined as the vectors that have magnitude equal to 1 and directions lying along the x, y, and z axes. In speech, they are referred to as "x-hat" and so on.

A slightly different, and harder to remember, version of this notation is unfortunately more prevalent. In this version, the unit vectors are called