**Definition of a Vector:**
In this section, we identify a vector quantity by a letter with
an arrow on top such as
.
By definition, a vector is identified in terms of its magnitude and direction.

When we represent a vector graphically by an arrow, we identify its magnitude by the length of the arrow, and its direction by the angle between the arrow and a reference axis and the location of the arrow head or the sense of the vector. To help distinguish between the vector and its magnitude, we use the same symbol for magnitude but drop the arrow on top.

Therefore, for vector ,

- magnitude is defined by .
- direction is defined by θ and the arrow head (sense).