Chap12_Sec1

Chap12_Sec1 - VECTORS AND THE GEOMETRY OF SPACE 12.1...

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12.1 Three-Dimensional oordinate Systems VECTORS AND THE GEOMETRY OF SPACE Coordinate Systems In this section, we will learn about: Aspects of three-dimensional coordinate systems.

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THREE-DIMENSIONAL (3-D) COORDINATE SYSTEMS To locate a point in space, three numbers are required. We represent any point in space by an ordered triple ( a , b , c ) of real numbers. In order to represent points in space, we first choose: s A fixed point O (the origin) s Three directed lines through O that are perpendicular to each other The three lines are called the coordinate axes. They are labeled: x -axis, y -axis and xis. Usually, we think of: z -axis. Usually, we think of: s The x - and y -axes as being horizontal s The z -axis as being vertical We draw the orientation of the axes as shown. The direction of the z -axis is determined by the right-hand rule, illustrated as follows. Your thumb points in the positive direction of the z -axis.
Now, if P is any point in space, let: s a be the (directed) distance from the

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This note was uploaded on 02/23/2010 for the course MATH 221 taught by Professor Staff during the Spring '08 term at Tulane.

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Chap12_Sec1 - VECTORS AND THE GEOMETRY OF SPACE 12.1...

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