Calculus Notes 13.1 - Calculus-Stewart Dr. Berg Summer 09...

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Calculus- Stewart Dr. Berg Summer ‘09 Page 1 13.1 13.1 Three-Dimensional Coordinate Systems To locate a point in the plane, two numbers are necessary. Hence, we say that a plane has two degrees of freedom, or is two-dimensional. By convention, a point with coordinates ( x , y ) is graphed in a coordinate system with the first coordinate located along a horizontal number line through an origin with numbers increasing from left to right, and the second coordinate located along a vertical number line with numbers increasing from below to above. The coordinates of a plotted point are found by extending perpendiculars to the axes, which are at a right angle to each other. To locate points in three-dimensional space, we need three numbers ( x , y , z ). The graphic representation is in a coordinate system with the positive x -axis pointing toward you, the y -axis pointing to the right, and the z -axis pointing up. These are the coordinate axes . Contained within three-dimensional real space (usually designated
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Calculus Notes 13.1 - Calculus-Stewart Dr. Berg Summer 09...

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