Example 5

A triangle has vertices (0, 0), (2, -1), and (3, 1) (Figure 10.1.19). Find the vectors counterclockwise around the perimeter of the triangle and check that their sum is the zero vector.

Figure 10.1.19

The three vectors are

A = (2 - 0)i + (- 1 - 0)j = 2i - j,

B = (3 - 2)i + (1 - (-1))j = i + 2j,

C = (0 - 3)i + (0 - 1)j = -3i - j.

Their sum is

A + B + C = (2 + 1 - 3)i + (-1 + 2 + (-1l))j = 0i + 0j.