Engineering Calculus Notes 80

Engineering Calculus Notes 80 - 2 y + 4 z = 0 , so any...

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68 CHAPTER 1. COORDINATES AND VECTORS Given a linear equation, we can parametrize its locus by fnding three noncollinear points on the locus and using the procedure above. For example, to parametrize the plane given by 3 x 2 y + 4 z = 12 we need to fnd three noncollinear points in this plane. I± we set y = z = 0 , we have x = 4 , and so we can take our basepoint P to be (4 , 0 , 0), or −→ p 0 = 4 −→ ı . To fnd two other points, we could note that i± x = 4 then
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Unformatted text preview: 2 y + 4 z = 0 , so any choice with y = 2 z will work, or example Q (4 , 2 , 1), or v = PQ = 2 + k gives one such point. Unortunately, any third point given by this scheme will produce w a scalar multiple o v , so wont work. However, i we set x = 0 we have 2 y + 4 z = 12 , and one solution o this is y = 4 , z = 1 ,...
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