Example 3

The vectors

A = 2i, B = 2i + εj, C = -εi + ε²j

are almost parallel to each other (Figure 10.8.3). Their unit vectors are

Figure 10.8.3

Let A ≠ 0 be a hyperreal vector with unit vector U = A/|A|. A is almost parallel to the real unit vector st(U). Thus every nonzero hyperreal vector is almost parallel to a real vector.