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Math 224 – Calculus III
1
12.1 ThreeDimensional Coordinate Systems
Recommended Homework: #139 (odds)
Until now in calculus, we have been working in a 2D system:
Points in the plane are located by ordered pairs:
( , )
xy
The two axes divide the (infinite) plane into 4 quadrants
Notation:
or
2
Also called a Cartesian “product”
An equation that involves
x
and
y
defines a
curve
in the plane
2
The ThreeDimensional Coordinate System
Picture:
Points in space are located by
ordered triples
:
( , , )
x y z
The three axes divide space into 8
octants
Notation:
or
3
Also called a Cartesian product
Note: The „old‟
plane is now lying flat with the positive
x
axis coming out of the page
towards you
Can you visualize the
xz
plane?
The
yz
plane?
An equation that involves
,
and
z
defines a
surface
in
3
x
y
z
y
x
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View Full Document Math 224 – Calculus III
2
Example:
Locate the points
( 2, 5, 4)
A
and
(3, 0, 5)
B
on the 3D coordinate system:
Example:
What is the projection of the point
( 5, 2, 6 ) on the
xy
plane?
The
xz
plane?
The
yz
plane?
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This note was uploaded on 10/31/2010 for the course MATH 224 taught by Professor Harris during the Fall '09 term at Illinois Central.
 Fall '09
 Harris
 Calculus

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