BSNS102 Study Guide - Final Guide: Global Positioning System, Coordinate Space, Dot Product
28 Jan 2021
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The previous figure provides geometric evidence that vector addition is commutative, but vector subtraction is not. Notice that the vector labeled a+b is identical to the vector labeled b+a, but the vectors d c and c d point in opposite directions because d c = (c d). The triangle rule can be extended to more than two vectors. Figure 5. 7: extending the triangle rule to more than two vectors. Armed with the triangle rule, we can now verify something mathematically that we stated geomet- rically in section 4. 2. 4: a vector can be interpreted as a sequence of axially aligned displacements. Figure 5. 8 is a reproduction of figure 4. 5, which shows how the vector [1, 3, 4] may be inter- preted as a displacement of one unit to the right, three units down, and then four units forward: Figure 5. 8: interpreting a vector as a sequence of displacements. We can interpret figure 5. 8 mathematically using vector addition:
