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The coordinate surfaces of the Cartesian coordinates (x, y, z). The z-axis is vertical and the x-axis is highlighted in green. Thus, the red plane shows the points with x = 1, the blue plane shows the points with z = 1, and the yellow plane shows the points with y = −1.
A three-dimensional coordinate system is created by adding a new axis, called the z-axis, to the familiar xy-coordinate system. The new z-axis is inserted through the origin perpendicular to the x- and y-axes (Figure 13.25).
definition. The three-dimensional rectangular coordinate system consists of three perpendicular axes: the x x -axis, the y y -axis, and the z z -axis. Because each axis is a number line representing all real numbers in R R the three-dimensional system is often denoted by R3 R 3.
Cartesian coordinates of three-dimensional space. In three-dimensional space, the Cartesian coordinate system is based on three mutually perpendicular coordinate axes: the x x -axis, the y y -axis, and the z z -axis, illustrated below. The three axes intersect at the point called the origin.
1. The xyz Coordinate Axis System. The xyz coordinate axis system, denoted 3, is represented by three real number lines meeting at a common point, called the origin. The three number lines are called the x-axis, the y-axis, and the z-axis. Together, the three axes are called the coordinate axes.
The three directions in the Cartesian coordinate system are specified as the axes X, Y, and Z. The axes are mutually perpendicular and intersect at one point: the datum (origin). An absolute coordinate designates the distance to the datum along a single axis.
The z -axis is perpendicular to both the x -axis and the y -axis. This demo illustrates a 3D coordinate system. The positive directions of the x, y, and z axes are shown as big arrows. The x -axis is green, the y -axis is blue, and the z -axis is red. You can drag on the axes to rotate the image. 3D Axes. Sorry, an error occurred:
