**Introduction to Three–dimensional Geometry: Coordinates of a point**

In a 3D plane, assume that P is any point in space. In this place, let a be the (directed) distance from the yz-plane to P, let b be the distance from the xz-plane to P, and let c be the distance from the xy-plane to P. We represent the point P by the ordered triplet (a, b, c), where a,b and c are real numbers. Therefore, a, b, and c are the coordinates of P. Therefore, the location of point P(*a*, *b*, *c*) can be marked by mapping the XYZ octant. For this purpose, we begin at the origin *O* and move *a *units along the *x*-axis, then *b *units parallel to the *y*-axis, and then *c *units parallel to the *z*-axis as shown in the figure below:

The point *P*(*a*, *b*, c) determines a rectangular box as in the figure below. We start by drawing a perpendicular from *P *to the *xy*-plane to get point *Q* with coordinates (*a*, *b*, 0). Point Q is called the projection of *P *onto the *xy*-plane. Similarly, *R*(0, *b*, *c*) and *S*(*a*, 0, *c*)are the projections of *P *onto the *yz*-plane and *xz*-plane, respectively as shown in the figure below.

The Cartesian product of R^{3} = RR** R**= {(*x*, *y*, *z*) | *x*, *y*, *z *R }has ordered triples of real numbers. We can give an individual correspondence between points *P *in space and ordered triples (*a*, *b*, *c*) in R^{3}. This formation of this ordered triplet is called a three-dimensional rectangular coordinate system. Here, the first octant can be explained as the set of points whose coordinates are all positive.In 2D analytic geometry, the graph of an equation involving *x* and *y *is a curve in R^{2} while in 3D, an equation in *x*, *y*, and *z* represents a *surface *in R^{3}.

The equation *z* = 3 represents the set {(*x*, *y*, *z*) | *z* = 3}, which is the set of all points in R^{3} whose *z*-coordinate is 3.In general, if *k* is a constant, then *x* = *k* represents a plane that is parallel to the *yz*-plane, *y* = *k* is a plane parallel to the *xz*-plane, and *z* = *k* is a plane that is parallel to the *xy*-plane. In the figure below, the faces of the rectangular box are formed by the three coordinate planes *x* = *a*, *y* = *b*, and *z* = *c* and *x* = 0 in the *yz*-plane, *y* = 0 in the *xz*-plane, and *z* = 0 in the *xy*-plane.