



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
is there industrial application of fullrenes.
What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
sciencedirect big data base
Ernesto
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
How can I make nanorobot?
Lily
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
how can I make nanorobot?
Lily
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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