Unit Vector

The unit vector of A is defined as

As in the two-dimensional case, the components of U, shown in Figure 10.3.5, are the direction cosines of A,

U = cos αi + cos βj + cos γk.

Figure 10.3.5(a) & (b)

Again, A is determined by its length and direction cosines, and the sum of the squares of the direction cosines is one,

A = |A| cos αi + |A| cos βj + |A| cos γk, cos² α + cos² β + cos² γ = 1.

Example 3 Finding the Unit Vector