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The right-hand rule

For a "right-handed" coordinate system, the direction of the resultant vector for AxB can be determined as follows:

Point the forefinger of the right hand in the direction of A and point the second finger in the direction of B. The thumb will then point in the directionof the resultant vector.

The cross product is not commutative

If you think about this, you should realize that the cross product is not commutative. That is to say that AxB is not the same as BxA because thedirection of the resultant vector would not be the same.

Create a vector diagram on your graph board

Once again, in order for you to better understand the nature of a vector cross product, I recommend that you create a Cartesian coordinate system on yourgraph board, and draw the following two vectors.

A vector diagram for your graph board

Draw the first vector from the origin to a point at x = 1y = 1.73 Label this vector A.Draw a second vector from the origin to a point at x = 2.9y = 0.78 Label this vector B.

The cross product

The cross product, AxB is defined as

AxB = Amag*Bmag*sin(angle)

where

  • Amag is the magnitude of the vector A
  • Bmag is the magnitude of the vector B
  • angle is the angle between the two vectors, which must be less than or equal to180 degrees

The area of the parallelogram

Use the vectors that you have drawn on your graph board to construct a parallelogram and see if you can estimate the area of that parallelogram.

Even if you were a sighted student having the parallelogram drawn on high-quality graph paper, it would be something of a chore to manuallydetermine the area of the parallelogram.

Let's work through some numbers

Let's use the cross product to determine the area of the parallelogram.

Given the definition of the cross product, we see that there are three values that we need:

  • Amag
  • Bmag
  • angle

Same vectors as before

If we were starting out with two new vectors, we could compute the magnitude of each vector using the Pythagorean theorem. We could also determine the angleby computing the vector dot product that I explained earlier in this module.

As you may have noticed, these are the same two vectors that we used earlier, and we computed those three values earlier. Going back and recovering thosethree values, we have

  • Amag = 2.0
  • Bmag = 3.0
  • angle = 45 degrees (at least that is what I intended for it to be)

The area of the parallelogram

Using the earlier definition and the nomenclature for the Google calculator,

AxB = Amag*Bmag*sin(angle), or

AxB = 2.0*3.0*sin(45 degrees), or

AxB = 4.24 square units

The direction of the resultant vector

If you place the end of your thumb at the origin of your Cartesian coordinate system, you should be able, with reasonable comfort, to point your forefinger inthe direction of A and your second finger in the direction of B.

According to the right-hand rule , this means that the direction of the resultant vector is the direction that your thumb ispointing, or straight down into the graph board.

Perpendicular or parallel vectors

Now consider what happens as the angle varies between 90 degrees (perpendicular vectors) and 0 degrees (parallel vectors) for a given pair ofvectors.

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, 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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