The line can be considered as the track of a moving particle with position X at time t given by
Here is an example of a vector-valued function of a real variable, i.e.,
The scalar t is often called a parameter and (2.1) a vector parametric equation, or simply, a vector equation of the line .
Consider a line passing through points P and Q. By theorem 2.4, it can be written as so that (2.1) becomes
which means since . Hence, 2 points on the line are distinct iff their parameters are distinct.
Consider 3 points , and . We say is between and if or .
A pair of points P and Q are congruent to another pair P' and Q' if . The norm is called the distance between P and Q.