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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).
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.
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.
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.
x -axis is the horizontal axis. y -axis is the vertical axis. A point in the plane is defined as an ordered pair, (x,y) (x, y), such that x is determined by its horizontal distance from the origin and y is determined by its vertical distance from the origin. Example: Plotting Points in a Rectangular Coordinate System.
One way to define the direction of a three-dimensional vector is by using direction cosine angles, also commonly known as coordinate direction angles. The direction cosine angles are the angles between the positive x, y, and z axes to a given vector and are traditionally named θx, θy, and θz.
