12.1 - Section 13.1 Three-Dimensional Coordinate Systems...

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Unformatted text preview: Section 13.1 Three-Dimensional Coordinate Systems Living in a 3-dimensional World 1. Three-Dimensional Rectangular Coordinate System We can sketch the graph of a function of two variables in the plane: the x-coordinate is the input value and the y coordinate is the corre- sponding output. To illustrate the graph of a function of two variables, we need two inputs and a single output - this means we need an extra dimension if we want to sketch a graph. We do this as following: (The right hand rule) With your right hand, point your thumb up, and your next finger and your middle finger outward per- pendicular to each other. Draw three lines in the direction your thumb and fingers are pointing - label the line along your thumb the z-axis, your middle finger the y-axis and the re- maining one the x-axis. The positive axis is in the direction your fingers point. z x y Any point P in 3 space is completely determined by its distance along the x , y and z-axis. In order to sketch a point P in 3- space, we associate the ordered triple ( a, b, c ) where P is a directed distance of a units in the x-direction, b units in the y- direction, and c units in the z-direction. We will often denote a point P as P ( a, b, c ) or ( a, b, c ). We call the three axis the coordinate axis ....
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This note was uploaded on 10/28/2010 for the course MA 261 taught by Professor Stefanov during the Fall '08 term at Purdue University-West Lafayette.

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12.1 - Section 13.1 Three-Dimensional Coordinate Systems...

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