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The two lines and the two vectors should now form a parallelogram. In other words, you should now have four pins located at the four corners of aparallelogram.

Solving for the resultant vector

According to the parallelogram law, the resultant vector, vecAC, is represented by a directed line that extends from point A to the intersection ofthe two lines that you constructed earlier. In other words, the sum of the two vectors is equal to a diagonal line that extends from the starting point to theopposite corner on the parallelogram that you constructed.

Subtracting vectors

In normal arithmetic subtraction, a subtrahend is subtracted from a minuend to find a difference .

To subtract a subtrahend vector from a minuend vector (in a plane), add 180 degrees to the direction of the subtrahend vector, causing it to point in theopposite direction, and add the modified subtrahend vector to the minuend vector.

If you subtract vecAB in the above example from vecBC, you should be able to show that the difference vector is represented by the other diagonal in theparallelogram. However, you will probably find it easier to do this mathematically rather than doing itgraphically.

Mathematical solutions

The horizontal component of the sum of two or more vectors is the sum of the horizontal components of the vectors.

The vertical component of the sum of two or more vectors is the sum of the vertical components of the vectors.

The horizontal and vertical components

The horizontal and vertical components respectively of a vector vecAB are equal to

  • vecABh = vecABmag * cos(angle)
  • vecABv = vecABmag * sin(angle)

where

  • angle is the angle that the vector makes relative to the horizontal axis.
  • vecABh, vecABv, and vecABmag are respectively the horizontal component, the vertical component, and the magnitude of the vector vecAB

The magnitude of the resultant vector

Given the horizontal and vertical components of the resultant vector, the magnitude of the resultant vector can be found using the Pythagorean theorem asthe square root of the sum of the squares of the horizontal and vertical components.

The angle of the resultant vector

The angle that the resultant vector makes with the horizontal axis is the arctangent (corrected for quadrant) of the ratio of the vertical component tothe horizontal component.

Using the Math.atan method

We will need to deal with several issues that arise when using the Math.atan method. Therefore, I will write a script that contains a function to deal with those issues. Then we can simply copy that function intofuture scripts without having to consider those issues at that time.

Please copy the code shown in Listing 1 into an html file and open the file in your browser.

Listing 1 . Using the Math.atan method.
<!-- File JavaScript01.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//Test for a range of known angles. var angIn = 0;var angOut = 0; var x = 0;var y = 0; while(angIn<= 360){ x = Math.cos(angIn*Math.PI/180);y = Math.sin(angIn*Math.PI/180); angOut = getAngle(x,y).toFixed(1);document.write("angle = " + angOut + "</br>"); angIn = angIn + 30;}//end while loop document.write("The End")</script></body></html>

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
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
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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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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