Vectors can be graphically represented by directed line segments. The length is chosen, according to some scale, to represent the magnitude of the vector, and the direction of the directed line segment represents the direction of the vector. For example, if we let 1 cm represent 5 km/h, then a 15-km/h wind from the northwest would be represented by a directed line segment 3 cm long, as shown in the figure at left.
A vector in the plane is a directed line segment. Two vectors are equivalent if they have the same magnitude anddirection.
Consider a vector drawn from point A to point B. Point A is called the initial point of the vector, and point B is called theterminal point. Symbolic notation for this vector is (read “vector AB”). Vectors are also denoted by boldface letters such as u, v, and w. The four vectors in the figure at left have the same length and direction. Thus they represent equivalent vectors; that is,
In the context of vectors, we use = to mean equivalent.
The length, or magnitude, of is expressed as ||. In order to determine whether vectors are equivalent, we find their magnitudes and directions.