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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).
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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.
Definition. The three-dimensional rectangular coordinate system consists of three perpendicular axes: the x -axis, the y -axis, the z -axis, and an origin at the point of intersection (0) of the axes. Because each axis is a number line representing all real numbers in ℝ, the three-dimensional system is often denoted by ℝ3.
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).
