Example 1: A Line Trough Two Points

Find a vector equation for the line through the two points A(2, 1) and B(-4,0), shown in Figure 10.2.7. The vector D = B - A from A to B is given by

D = (-4 - 2)i + (0 - l)j = -6i - j.

Figure 10.2.7

Since A is a position vector and D a direction vector of the line, the line has the vector equation

X = A + tD

= 2i + j + t(-6i - j).