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12.1
ThreeDimensional
oordinate Systems
VECTORS AND THE GEOMETRY OF SPACE
Coordinate Systems
In this section, we will learn about:
Aspects of threedimensional coordinate systems.
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View Full Document THREEDIMENSIONAL (3D) COORDINATE SYSTEMS
To locate a point in space, three numbers are required. We represent any point in
space by an ordered triple (
a
,
b
,
c
) of real numbers.
In order to represent points in space, we first choose:
s
A fixed point
O
(the origin)
s
Three directed lines through
O
that are perpendicular to each other
The three lines are called the coordinate axes. They are labeled:
x
axis,
y
axis and
xis. Usually, we think of:
z
axis. Usually, we think of:
s
The
x
 and
y
axes as being horizontal
s
The
z
axis as being vertical
We draw the orientation of the axes as
shown. The direction of the
z
axis is
determined by the righthand rule, illustrated
as follows. Your thumb points in the positive
direction of the
z
axis.
Now, if
P
is any point in space, let:
s
a
be the (directed) distance from the
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This note was uploaded on 02/23/2010 for the course MATH 221 taught by Professor Staff during the Spring '08 term at Tulane.
 Spring '08
 staff
 Vectors

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