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Finally Listing 2 calls the document.write method several times in succession to display the values stored in some of the variables mentioned above in thebrowser window as shown in Figure 12 . As you can see, the magnitude and angle of the resultant agrees with the estimate that I made using the graphic methodearlier.

Subtracting vectors

To subtract one vector from another using the mathematical approach, simply reverse the algebraic sign on the horizontal and vertical components for thesubtrahend vector and perform the addition shown in Listing 2 .

Adding more than two vectors

Let's work through a problem that requires the addition of four vectors.

A graphical solution

First I would like for you to lay out the vectors, tail-to-head on your graph board to create a solution to this problem.

Pretend that you take a walk consisting of the following sequential segments. Angles are specified relative to east with east being zero degrees. Positiveangles are counter-clockwise and negative angles are clockwise.

The segments are as follows:

  • 12 meters at 20 degrees
  • 8 meters at 120 degrees
  • 10.5 meters at -74 degrees
  • 12.5 meters at 145 degrees

What is your final displacement?

When you reach the end of the walk, what is your displacement (distance and direction) relative to the location at which you began the walk. You shouldbe able to do a reasonable job of measuring the displacement using your graph board.

A mathematical solution

Please copy the code shown in Listing 3 into an html file and open the html file in your browser.

Listing 3 . The sum of four vectors.
<!-- File JavaScript03.html --><html><body><script language="JavaScript1.3">//The purpose of this function is to receive the adjacent // and opposite side values for a right triangle and to// return the angle in degrees in the correct quadrant. function getAngle(x,y){if((x == 0)&&(y == 0)){ //Angle is indeterminate. Just return zero.return 0; }else if((x == 0)&&(y>0)){ //Avoid divide by zero denominator.return 90; }else if((x == 0)&&(y<0)){ //Avoid divide by zero denominator.return -90; }else if((x<0)&&(y>= 0)){ //Correct to second quadrantreturn Math.atan(y/x)*180/Math.PI + 180; }else if((x<0)&&(y<= 0)){ //Correct to third quadrantreturn Math.atan(y/x)*180/Math.PI + 180; }else{//First and fourth quadrants. No correction required. return Math.atan(y/x)*180/Math.PI;}//end else }//end function getAngle//Specify the magnitudes and angles of four vectors. //Convert the angles from degrees to radians.var vecAmag = 12; var vecAang = 20*Math.PI/180;//degrees*radians/degrees=radiansvar vecBmag = 8; var vecBang = 120*Math.PI/180;//degrees*radians/degrees=radiansvar vecCmag = 10.5; var vecCang = -74*Math.PI/180;//degrees*radians/degrees=radiansvar vecDmag = 12.5; var vecDang = 145*Math.PI/180;//degrees*radians/degrees=radians//Compute the horizontal and vertical components of each vector. var vecAh = vecAmag*Math.cos(vecAang);var vecAv = vecAmag*Math.sin(vecAang); var vecBh = vecBmag*Math.cos(vecBang);var vecBv = vecBmag*Math.sin(vecBang); var vecCh = vecCmag*Math.cos(vecCang);var vecCv = vecCmag*Math.sin(vecCang); var vecDh = vecDmag*Math.cos(vecDang);var vecDv = vecDmag*Math.sin(vecDang); //Compute the sums of the horizontal and vertical components from// the four vectors to get the horizontal and vertical component // of the resultant vector.var vecResultH = vecAh + vecBh + vecCh + vecDh; var vecResultV = vecAv + vecBv + vecCv + vecDv;//Use the Pythagorean theorem to compute the magnitude of the// resultant vector. var vecResultMag = Math.sqrt(Math.pow(vecResultH,2) +Math.pow(vecResultV,2)); //Compute the angle of the resultant vector.vecResultAng = getAngle(vecResultH,vecResultV); document.write("Hello from JavaScript" + "</br>") document.write("vecResultMag = " + vecResultMag.toFixed(2) + "</br>"); document.write("vecResultAng = " + vecResultAng.toFixed(2) + "</br>"); document.write("The End")</script></body></html>

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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