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...
View
Full Document
 Fall '08
 ALL
 Calculus, Vectors, Elementary algebra, vertical line segments, right sides

Click to edit the document details