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10 Νοε 2020 · We denote the Euclidean plane by R2; the "2'' represents the number of dimensions of the plane. The Euclidean plane has two perpendicular coordinate axes: the x -axis and the y -axis. In vector (or multivariable) calculus, we will deal with functions of two or three variables (usually x, y or x, y, z, respectively).
A three dimensional Cartesian coordinate system, with origin O and axis lines X, Y and Z, oriented as shown by the arrows. The tick marks on the axes are one length unit apart. The black dot shows the point with coordinates x = 2, y = 3, and z = 4, or (2, 3, 4).
The three-dimensional coordinate system contains an origin (normally denoted by O) and formed by three mutually perpendicular coordinate axes: the x -axis, y -axis, and the z -axis.
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In three dimensions, we define coordinate planes by the coordinate axes, just as in two dimensions. There are three axes now, so there are three intersecting pairs of axes. Each pair of axes forms a coordinate plane: the xy x y -plane, the xz x z -plane, and the yz y z -plane (Figure 5).
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).
