The 3D Coordinate System
We’ll start the chapter off with a fairly short discussion introducing the 3D coordinate
system and the conventions that we’ll be using. We will also take a brief look at how
the different coordinate systems can change the graph of an equation.
Let’s first get some basic notation out of the way. The 3D coordinate system is often
denoted by
. Likewise the 2D coordinate system is often denoted by
and the 1D coordinate system is denoted by
. Also, as you might have guessed
then a general
n
dimensional coordinate system is often denoted by
.
Next, let’s take a quick look at the basic coordinate system.
This is the standard placement of the axes in this class. It is assumed that only the
positive directions are shown by the axes. If we need the negative axis for any reason
we will put them in as needed.
Also note the various points on this sketch. The point
P
is the general point sitting out
in 3D space. If we start at
P
and drop straight down until we reach a
z
coordinate of
zero we arrive at the point
Q
. We say that
Q
sits in the
xy
plane. The
xy
plane
corresponds to all the points which have a zero
z
coordinate. We can also start
at
P
and move in the other two directions as shown to get points in the
xz
plane (this
is
S
with a
y
coordinate of zero) and the
yz
plane (this is
R
with an
x
coordinate of
zero).
Collectively, the
xy
,
xz
, and
yz
planes are sometimes called the coordinate planes. In
the remainder of this class you will need to be able to deal with the various coordinate
planes so make sure that you can.
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 Fall '08
 prellis
 Cartesian Coordinate System, Euclidean geometry, Polar coordinate system, coordinate

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