Cross product 1 | Magnetic forces, magnetic fields, and Faraday's law | Physics | Khan Academy

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Introduction to the cross product. Created by Sal Khan.
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[@jimumele4984]

why do we even need school when we have khan academy (internet institution).......thanks

[@risklife4527]

True bro

[@sumikajuutilainen1534]

Because there are some things that khan academy cannot answer but textbooks can.

[@parthokarmaker5043]

@@sumikajuutilainen1534 you cant understand khan academy actually

[@nilatstc]

I didn't quite get the cross product for the past 7 years and I managed to understand it in just 10 mins of this video.... Great job!

[@isidoracocanovic1590]

Thx bro, you explained it better than 2 of my teachers and a couple of colleagues. Ty so much ^^

[@flyhalfinoz]

thank you!! u saved me from an eternal confusion of the scalar/vector product!!

[@sundriedturd]

I had a lengthy conversation with my physics professor when I asked the same question. The right hand rule is merely convention. The resultant force doesn't actually pop out perpendicularly. In the case of torque, it merely helps describe the direction of rotation around an axis, and the plane through which the object is rotating. The attributes of the plane and direction of rotation are easier to communicate if you give torque a z component. I hope this helps.

[@MrUnladenswallow]

7:36 i like where this is going

[@allanfernz9356]

youtube......plzz let this man do his work......he is doing an amazing job!!!

[@Anushka2704]

thank you for the explanation Sir!

[@musicandmeareinlove]

@xxilikemustardxx yep i did let A and B be two vectors A=xi + yj + zk and B= ai + bj + ck now, A*B =A B sin (theeta) n (n gives the direction) find the magnitude of A*B using the matrix method and equate it to A B sin (theeta) you'll get the value of sin (theeta) then look uo in the log table and u'll get the vlue of theeta...

[@jimkeller3868]

Nobody seems to explain this conceptually well. Yes he mentioned this is in 3 dimensions. If we only have two vectors A and B, why is a third dimension necessary? Why is n always orthogonal to A and B? What exactly does the cross product mean?

[@andrzejgieralt9872]

um you take a vector that is perfectly perpendicular to both vectors at once, i think but im not sure. Like if axb = c then c is the vector that is perpendicular to both. but idk.

[@DeFreshS10]

it is hard to see here but if you look for a right hand rule video that applies to electromagnetism you will see why we need 3 dimensions. For electricity to be generated by magnets, the magnetic field needs to be orthogonal to the direction of the electrons, the n vector.

[@DnBastard]

if you draw X and Y on a piece of wood, then stick a knife into where they originate, that knife is the cross product. Rotate the wood all you want, the knife will always show the cross product.

[@ankitaaarya]

Nobody seems to understand your question, but i know what are you talking about. I wish i could explain it t you, what cross product and dot product really is.

[@Barnekkid]

That was very clear, especially the part about the right hand rule.

[@bigmosofly]

you just saved me from failing my statics test. thank you!!!

[@9742R]

ur a very great man sal ! ur great ! u help us ppl in india to learn what we want too and not by heart the crap which they teach in school ! respect u loads brother !

[@boachiedarkwabenjamin5791]

With Khan Academy, what is lectures? All you need is internet

[@divvy1400yam600]

There is no doubt whatsoever that your videos are informative. But my word ...do you over elaborate. !

[@joelprada5056]

Thanks! Very helpful. Just one observation...minute 5:12 the answer is 7.5 not 25. I think you forgot to divide by two (or multiply by 1/2)

[@TheBarbaricFisherman]

Joel Prada 5 time 10 is 50. 50 divided by 2 is 25

[@boachiedarkwabenjamin5791]

Thank you

[@pimp33040]

Amazing video, way better than my Physics "professor" in college.

[@PrecariousCreations]

Good.

[@beastlt12]

Excellent. Exactly what I was looking for.

[@Peter_1986]

05dabest One radian (rad) is an angle where the arc length of the circle has the same length as the radius. One full circle is therefore exactly 2*pi rad = 360°, and if you divide both sides by 12 you get that pi/6 rad = 30°.

[@musicandmeareinlove]

@RJonStreetz lol...wt if u're just given the coordinates...? in d form A=xi + yj + zk and B= ai + bj + ck and asked to find the angle betn them? u cant always draw the vectors on d cartesian plane and measure the angle between em...

[@sundriedturd]

as for why it's the right (and not left) hand, i would imagine it's because most people are right handed, and it's a simple way to remember which direction it is.

[@narutosramenbuddy]

i enjoyed the bonus lesson on arrows.

[@pragatiarora3568]

thank u so much sir :)

[@tejasgokhale01]

On what basis did we decide this thumb rule to determine direction? How can something just popup in different dimension? and why only right hand rule? why not say left hand rule? this is bugging me for a while now so got to know it.

[@ELECTRIC67100]

khan as excellent as always in his explanation

[@DJAPG90]

Same thing I am trying to find out.

[@RJonStreetz]

@musicandmeareinlove Angle?? What do you mean? Just use a protractor. Or am I missing something??

[@memirandawong]

.....this concept sounded mysterious and difficult until I watched this video...

[@gaypotter]

u are great at teaching, thanks!

[@sopro671]

Thanks really helped alot

[@petrichorpse]

Hi kahn! Im a big fan of your videos, and I know you have a ton on your hands already, but maybe you should redo your videos with lower quality?

[@playman350]

Lower or higher? :o

[@jamescarmody4713]

His videos _which have_ lower quality. For the record, Sal did just that: www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/linear-algebra-cross-product-introduction

[@zailuanshuoyou955]

why your thumb is going down in this gesture. well, the final direction is into the page. Is it because the thumb point the direction of the screen? The arrow is going towards the screen or moving away of me. From my perspective, I can see the end of the arrow moving away from me. It can be noted by a circle with the cross in the middle.

[@zailuanshuoyou955]

hope im not getting anything wrong but 'into the page out of the page' things are turely bothering me

[@brco2003]

You should give yourself more credit with your artistic abilities; your work is really good.

[@deepak8022]

Why we write sin degree why not cos degree. What is the reason that in dot product degree is in cos and in cross product degree is in sin. Please someone tell me the reason.

[@primumdiscenti]

its because we require only one of the components of either the ''a'' or ''b'' vector. THe cos vector would be in the in the direction of the other vector. ie the ''cos zero = 1 '' and can be left out of the equation as the angle between the component vectors is 0 degrees.

[@lastshadowmonkeys]

Thanks so much! Great help this :D

[@altairservers5489]

1st Year University now; I still use your vids. =3

[@JimmyBatchelder]

How would this work if one was using three dimensional vectors?

[@SteveTheCart]

Wow!

[@RJonStreetz]

@musicandmeareinlove Oh yeah right...forgot about that....Thanks!

[@ryanflippin1243]

If angle theta was 235degrees would you take sin of that or would you take sin of 135degrees

[@musicandmeareinlove]

how do we find the angle between two vectors?

[@hasibmiraz5873]

upgrade the video quality

[@xXxSkyViperxXx]

he made a better one in the following year of this video's upload release with even a better drawing of the hand. the video is under the linear algebra, vectors and spaces track

[@Thmyris]

This video is from 2008 and this quality is pretty much the highest you could get back then.

[@andrewverdes80]

Really good

[@Master1906]

The university of Khan

[@siddharthachowdhuri1080]

Thank you :D you're great! Keep it up! :)

[@leemaines1541]

a unit vector is a vector with a length of 1 unit... whatever that unit might be.

[@Elzelgator]

awesome

[@HT-rq5pi]

you would take sin of 125, which is the smallest angle (360-235)

[@Yanman0]

if "n" points into the page. wouldn't the arrow be pointing up in your 3d diagram?

[@BoZhaoengineering]

I bet some of schools need badly khan Academy to improve their teaching in China. The point is those schools don’t feel they need to be improved and they think current education practice is permanent regime that never needs to adopt new ideas to overcome difficulties in learning & teaching. In fact the education regime is broken from itself.

[@abhishekmanral8501]

Best a great salute to you mr. 😱. Sorry sir✌✌✌✌

[@raqibshahzad3520]

GOOD VIDEO

[@_anbu_]

What is the role of sin here .

[@anuragsahoo94]

why sine?

[@freshely9309]

Why does it have to be the right hand?

[@Rand0mAsian]

@onetimeuse12 thats the dot product =)

[@bluewolf8085]

Appreciate the knowledge... Is this highschool or college work in your country? Anyone please comment highschool or college and your country. Thank you...

[@watermelonsugahiiiiiiiiiii3051]

In india thats 3rd year high school work.

[@seberinm7]

It is in grade 10 in our country means it it is in highschool

[@whyamidoingthis5083]

.....i stilll dont get it ;_;

[@radhikak747]

5:15 :D

[@TheNo1WarLord]

What if a=b (theta = 0) is your thumb out or in? What if a=-b (theta = 180) is your thumb out or in?

[@playman350]

In both cases sin(θ) = 0. So the cross product *a* x *b* is the nullvector.

[@DeFreshS10]

your assuming that equal lengths mean something and depend on theta.. they do not. The lengths of a or b do not depend on theta, only the angle between them. regardless of what a and b are, if sin(theta)=0 then the cross product doesnt exist.

[@xruan6582]

theta is more like 60 degree to me

[@themegacave]

but why though

[@KimJong7hrill]

@lseateal lol I don't have any fingers either.

[@onetimeuse12]

isn't the formula used with cos?

[@mrmoxx7820]

No

[@andrizee91]

@lseateal Use your toes.

[@MattOGormanSmith]

No you wouldn't, you'd always consistently use sin(B-A) to retain the sign of the sin, so the resulting cross product vector obeys the right hand rule.

[@mahnoormallano5806]

tell m how we can say it is negative and positive

[@bartcase]

@lseateal then how did you type this comment?

[@Ren520]

that was very concise.. i'm learning this prior to my fall class because im afraid it'll be too difficult. im sure i'll do great with your vids, in addition to MIT's OCW. by the way, you achieved and did so many great things in life, congrats!

[@crashonthehumble]

outstanding

[@ahsansiddiqui7708]

i dont understand unit vector does some explain me?

[@usharanikusuma1582]

ahsan siddiqui kouhkmp

[@dusttaker]

my fingers just split off! cant quite get index and middle finger to do that!

[@Anushka2704]

same here! had to twist my hand real hard to achieve that position.. : )

[@jinheepark6961]

isn't it cosine, not sine?

[@tallalaazmi1287]

cosine is in dot product

[@05dabest]

how did he convert 30 degrees to pi/6 rad's?

[@jamescarmody4713]

It's by definition. Degrees of a triangle on a unit circle move the radian measure. Here's a graph that shows degree, radians, and coordianates of points on a unit circle commons.wikimedia.org/wiki/File:Unit_circle_angles_color.svg

[@nandhannatarajan2127]

By definition, 180 degrees = pi rads.

[@infinitesimotel]

The wind changed as I was trying to do the hand rule now my fingers are stuck that way, HELP!

[@TheFutureIsRightHere]

I still didn't get the "Right hand rule" :p

[@musicandmeareinlove]

@RJonStreetz :)

[@xGlassChild]

My physics teacher keeps telling me to take the cross products of things in 2d?

[@wasanali551]

Arabic translate please

[@GenericMedusa99]

wait wuht?

[@punyomilo507]

How can one man know this much.. I mean he does every subject.

[@That_One_Guy...]

he is studying of course , and he doesnt teach every subject , sometimes there's people subtituting him in physic

[@wetim99]

i used to be good at math but then i took an arrow through the screen

[@zakaryakhan7139]

Y tube allow him man 😠😠😠😠

[@alperenozdemir1332]

thank you but IT IS GODDAM 240p YOU KNOW THAT RIGHT ?

[@andrewzhu5294]

MY GOOD SIR, THIS WAS UPLOADED IN 2008. YOU KNOW THAT RIGHT?

[@ramiBudemaris]

you explained nothing

[@hashmat187]

@lseateal how did you type this comment then