# 1.9 Game 2302-0125: vector addition

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Learn how to add two or more vectors. Also learn about the head-to-tail 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.

## 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 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.

## Figures

• 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 . Command-line 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 head-to-tail 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 game-math 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.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
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 a peer
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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