12.1 Three-Dimensional Coordinate Systems

12.1 - Math 224 Calculus III 12.1 Three-Dimensional Coordinate Systems Recommended Homework#1-39(odds Until now in calculus we have been working in

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Math 224 – Calculus III 1 12.1 Three-Dimensional Coordinate Systems Recommended Homework: #1-39 (odds) Until now in calculus, we have been working in a 2-D system: Points in the plane are located by ordered pairs: ( , ) xy The two axes divide the (infinite) plane into 4 quadrants Notation: or 2 Also called a Cartesian “product” An equation that involves x and y defines a curve in the plane 2 The Three-Dimensional Coordinate System Picture: Points in space are located by ordered triples : ( , , ) x y z The three axes divide space into 8 octants Notation: or 3 Also called a Cartesian product Note: The „old‟ plane is now lying flat with the positive x axis coming out of the page towards you Can you visualize the xz plane? The yz plane? An equation that involves , and z defines a surface in 3 x y z y x
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Math 224 – Calculus III 2 Example: Locate the points ( 2, 5, 4) A and (3, 0, 5) B on the 3-D coordinate system: Example: What is the projection of the point ( 5, -2, 6 ) on the xy plane? The xz plane? The yz plane?
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This note was uploaded on 10/31/2010 for the course MATH 224 taught by Professor Harris during the Fall '09 term at Illinois Central.

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12.1 - Math 224 Calculus III 12.1 Three-Dimensional Coordinate Systems Recommended Homework#1-39(odds Until now in calculus we have been working in

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