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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

Last Update: 2006-11-21