



Learn how to add two or more vectors. Also learn about the headtotail rule in vector addition, about the vector addition parallelogram, about the relationship between the length of the sum of vectors and the lengths of the individual vectors in the sum, how to add a vector to a point, how to get the length of a vector, and how to represent an object in different coordinate frames.
Table of contents
Preface
This module is one in a collection of modules designed for teaching
GAME2302 Mathematical Applications for Game Development at Austin
Community College in Austin, TX.
What you have learned
In the previous couple of modules, you learned:
 How to compare column matrices for equality
 How to compare two points for equality
 How to compare two vectors for equality
 How to add one column matrix to another
 How to subtract one column matrix from another
 How to get a displacement vector from one point to another
What you will learn
In this module you will learn:
 How to add two or more vectors
 About the headtotail rule in vector addition
 About the vector addition parallelogram
 About the relationship between the length of the sum of vectors and the
lengths of the individual vectors in the sum
 How to add a vector to a point
 How to get the length of a vector
 How to represent an object in different coordinate frames
Viewing tip
I recommend that you open another copy of this module in a separate
browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.

Figure 1 . Screen output from the program named VectorAdd01.

Figure 2 . Screen output from CoordinateFrame01 at startup.

Figure 3 . Screen output from CoordinateFrame01 after changes to the coordinate frame.

Figure 4 . Screen output from the program named VectorAdd02.

Figure 5 . Graphic screen output from the program named VectorAdd03.

Figure 6 . Commandline output from the program named VectorAdd03.

Figure 7 . Screen output from the program named VectorAdd04.

Figure 8 . Screen output from Exercise 1.

Figure 9 . Screen output from Exercise 2.
Listings

Listing 1 . The add method of the GM2D04.Vector class.

Listing 2 . The getLength method of the GM2D04.Vector class.

Listing 3 . The addVectorToPoint method of the GM2D04 class.

Listing 4 . Beginning of the program named VectorAdd01.

Listing 5 . Beginning of the method named drawOffScreen.

Listing 6 . The method named setCoordinateFrame.

Listing 7 . Adding two vectors.

Listing 8 . Draw vecA in RED with its tail at the origin.

Listing 9 . Draw vecB in GREEN headtotail with vecA.

Listing 10 . Draw sumOf2 in MAGENTA with its tail at the origin.

Listing 11 . Extending the example to three vectors.

Listing 12 . The actionPerformed method.

Listing 13 . The setCoordinateFrame method.

Listing 14 . Beginning of the drawOffScreen method.

Listing 15 . Define a point to position the vectors.

Listing 16 . Remaining code in the drawOffScreen method.

Listing 17 . Beginning of the method named drawOffScreen of the program named VectorAdd02.

Listing 18 . Do the same operations in a different order.

Listing 19 . Source code for the gamemath library named GM2D04.

Listing 20 . Source code for the program named VectorAdd01.

Listing 21 . Source code for the program named CoordinateFrame01.

Listing 22 . Source code for the program named VectorAdd02.

Listing 23 . Source code for the program named VectorAdd03.

Listing 24 . Source code for the program named VectorAdd04.
Questions & Answers
anyone know any internet site where one can find nanotechnology papers?
Introduction about quantum dots in nanotechnology
nano basically means 10^(9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
Difference between extinct and extici spicies
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Source:
OpenStax, Game 2302  mathematical applications for game development. OpenStax CNX. Jan 09, 2016 Download for free at https://legacy.cnx.org/content/col11450/1.33
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