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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.

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 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
  • 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.

Questions & Answers

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
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
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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