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Theorem 1
THEOREM 1 All the rules for vector algebra given in Section 10.1 hold for vectors in three dimensions. These rules are in Theorems 1, 2, and 3 of Section 10.1, and include the Triangle Inequality. In space, there are three basis vectors, denoted by i, j, and k. i has components (1, 0, 0), j has components (0, 1, 0), and k has components (0, 0, 1). i, j, and k are shown in Figure 10.3.4. As in the case of two dimensions, we see that ai + bi + ck is the vector in three dimensions with components a, b, and c. The rules for computing vectors by their components take the following form in three dimensions.
Basis vectors Figure 10.3.4
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Last Update: 2006-11-21