Vector
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Vector
To introduce rectangular coordinates in three-dimensional space, we begin with a plane on which we have set up a rectangular coordinate system O-xy in the usual manner. Through the point O, which we continue to call the origin, we pass a third line, perpendicular to the other two. This third line we call the z-axis. We assign coordinates to the z-axis using the same scale as used on the x- and y-axes, assigning the z-coordinate 0 to the origin O. For later convenience we orient the z-axis according to the right-hand rule: if the fingers of the right hand are curled from the positive x-axis toward the positive y-axis (the short route), the thumb points along the positive z-axis. (See Figure 13.1.1.)
y
Figure 13.1.1
The point on the x-axis with x-coordinate x0 is given space coordinates (x0, 0, 0); the point on the y-axis with y-coordinate y0 is given space coordinates (0, y0, 0); the point on the z-axis with z-coordinate z0 is given space coordinates (0, 0, z0).
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To introduce rectangular coordinates in three-dimensional space, we begin with a plane on which we have set up a rectangular coordinate system O-xy in the usual manner. Through the point O, which we continue to call the origin, we pass a third line, perpendicular to the other two. This third line we call the z-axis. We assign coordinates to the z-axis using the same scale as used on the x- and y-axes, assigning the z-coordinate 0 to the origin O. For later convenience we orient the z-axis according to the right-hand rule: if the fingers of the right hand are curled from the positive x-axis toward the positive y-axis (the short route), the thumb points along the positive z-axis. (See Figure 13.1.1.)
y
Figure 13.1.1
The point on the x-axis with x-coordinate x0 is given space coordinates (x0, 0, 0); the point on the y-axis with y-coordinate y0 is given space coordinates (0, y0, 0); the point on the z-axis with z-coordinate z0 is given space coordinates (0, 0, z0).
638
