12.1 Three-Dimensional Coordinate System
In
Cartesian coordinates
(or
rectangular coordinates
), a point
P
is referred to by three real
numbers, indicating the positions of the perpendicular projections from the point to three
fixed, perpendicular, graduated lines, called the
axes
. If the coordinates are denoted
x
,
y
,
z
, in
that order, the axes are called the
-axis
, etc., and we write
=(
,
,
). Often the
-axis is
imagined to be horizontal and pointing roughly toward the viewer (out of the page), the
-axis
also horizontal and pointing more or less to the right, and the
-axis vertical, pointing up. The
system is called
right-handed
if it can be rotated so the three axes are in this position. The
figure below shows a right-handed system. The point
=0,
=0,
=0 is the
origin
, where the
three axes intersect.
In Cartesian coordinates,
=(4.2,3.4,2.2).
If you drop a perpendicular from P to the xy-plane, we get a point Q with coordinate (a,b,0)