Engineering Calculus Notes 126

Engineering Calculus Notes 126 - (c) Now consider the three...

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114 CHAPTER 1. COORDINATES AND VECTORS x y z Figure 1.56: The Prism E (a) Show that E consists of all points in R 3 which simultaneously satisfy the inequalities x 0 y 0 x + y 1 0 z 1 . (b) Show that the six vertices of E are P 0 (0 , 0 , 0) P 1 (1 , 0 , 0) P 2 (0 , 1 , 0) Q 0 (0 , 0 , 1) Q 1 (1 , 0 , 1) Q 2 (0 , 1 , 1) . (Note that in this numbering, Q i is directly above P i .)
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Unformatted text preview: (c) Now consider the three oriented simplices 1 = P P 1 P 2 Q 2 = P 1 P 2 Q Q 1 3 = P 2 Q Q 1 Q 2 . Show that i. 1 consists of all points in E which also satisfy x + y + z 1 ....
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