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Engineering Calculus Notes 118

Engineering Calculus Notes 118 - 106 CHAPTER 1 COORDINATES...

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106 CHAPTER 1. COORDINATES AND VECTORS x y z O O P P Q Q R R −→ v Figure 1.54: square O PRQ We see from Figure 1.54 that the vectors −−→ O P , −−→ O Q , −→ v obey the right-hand rule, so have positive orientation. Given any four points A , B , C , and D in R 3 , we can form a “pyramid” built on the triangle ABC , with a “peak” at D (Figure 1.55 ). The A B C D Figure 1.55: Simplex ABCD traditional name for such a solid is tetrahedron , but we will follow the terminology of combinatorial topology, calling this the simplex 22 with vertices A , B , C and D , and denote it ABCD ; it is oriented when we pay attention to the order of the vertices. Just as for a triangle, the edges
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