Chapter 12, Problem 1GYR

To determine

Explain how the directed line segment in the plane represent the same vector.

Explanation of Solution

Description:

Generally, the vector is signified by the directed line segment $\overrightarrow{PQ}$ with initial point P and terminal point Q, and its length is denoted by $\left|\overrightarrow{PQ}\right|$. The two vectors are equal when they have same magnitude and direction.

Figure 1 shows the directed line segment in the plane represent the same vector.

In Figure 1, the four arrows represent in the plane is the directed line segment having the same length and direction. Therefore, the directed line segment can be written as follows.

$\overrightarrow{AB}=\overrightarrow{OG}=\overrightarrow{CD}=\overrightarrow{EF}$

Thus, the directed line segment in the plane represent the same vector is explained.