ThreeDtext

# ThreeDtext - ThreeD Coordinate Systems John E Gilbert...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ThreeD Coordinate Systems John E. Gilbert, Heather Van Ligten, and Benni Goetz The graph of a function f ( x, y ) of two variables is a surface in 3-space, and familiar single variable methods can be used once a coordinate system has been introduced into 3-space. The xyz-coordinate system in 3-space is obtained by adding the z-axis perpendicular to the usual xy-coordinate system in the xy-plane. Each point P in 3-space is then determined by a triple ( a, b, c ) as shown to the right. The three coordinate axes intersect at the origin, and each pair of axes determines a coordinate plane . If we drop a perpendicular from P to the the xy-plane, we get a point Q with coordinates ( a, b, 0) called the projection of P on the xy-plane. In the same way there are projections R (0 , b, c ) and S ( a, , c ) of P on the yz-plane and zx-plane respectively. x y z P ( a, b, c ) a b c The figures below show the three coordinate planes from two viewpoints : x y z 4 3 2 One Viewpoint: x, y, z > x y z 4 3 2-1 Another Viewpoint: x, z > , y < Colors help identify the coordinate planes: xy-plane { ( x, y, z ) : z = 0 } xz-plane { ( x, y, z ) : y = 0 } yz-plane { ( x, y, z ) : x = 0 } It will be important to understand planes parallel to the these coordinate planes....
View Full Document

## This note was uploaded on 06/05/2011 for the course MATH 408 D taught by Professor Gilbert during the Spring '11 term at University of Texas.

### Page1 / 5

ThreeDtext - ThreeD Coordinate Systems John E Gilbert...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online