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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

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris 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
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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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