Unformatted text preview: are mutually contradictory—the planes are parallel, and have no intersection. ±or example, the two equations x − 2 y + 3 z = 1 − 2 x + 4 y − 6 z = − 2 are equivalent (the second is the Frst multiplied by − 2) and describe a (single) plane, while x − 2 y + 3 z = 1 − 2 x + 4 y − 6 z = 0 are contradictory, and represent two parallel, nonintersecting planes. Oriented Volumes In common usage, a cylinder is the surface formed from two horizontal discs in space, one directly above the other, and of the same radius, by joining their boundaries with vertical line segments. Mathematicians...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Vectors

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