Unformatted text preview: orienting the base and taking the dot product of the generator with the oriented area of the base V = ± −→ v · ± A ( B ) . We can think of this dot product as the “signed volume” of the oriented cylinder, where the orientation of the cylinder is given by the direction of the generator together with the orientation of the base. The signed volume is positive ( resp . negative) if −→ v points toward the side of the base from which its orientation appears counterclockwise ( resp . clockwise)—in other words, the orientation of the cylinder is positive if these data obey the righthand rule. We will denote the signed volume of a cylinder C by −→ V ( C ). A cylinder whose base is a parallelogram is called a parallelepiped : this has three quartets of parallel edges , which in pairs bound three pairs of...
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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

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