Example 1: Vector Components

Find the components of the vectors represented by the given directed line segments.

(a)

x-component = 5 - 3 = 2, y-component = 1 - 2 = -1.

(b)

x-component = 2 - 0 = 2, y-component =-3-( - 2)= -1.

Notice that both of these directed line segments represent the same vector. They are shown in Figure 10.1.3.

Figure 10.1.3

Vectors are denoted by boldface letters, A. A vector is represented by a whole family of directed line segments. However, given a vector A and an initial point P, there is exactly one point 0 such that the directed line segment represents A. To find the x-coordinate of Q we add the x-coordinate of P and the x component of A; similarly for the y-coordinate.