What is a vector? - David Huynh

View full lesson: ed.ted.com/lessons/what-is-a-v...
Physicists, air traffic controllers, and video game creators all have at least one thing in common: vectors. But what exactly are they, and why do they matter? David Huynh explains how vectors are a prime example of the elegance, beauty, and fundamental usefulness of mathematics.
Lesson by David Huynh, animation by Anton Trofimov.

[@MewPurPur]

What are vectors? Me when doing physics: It's an arrow with a direction and magnitude. Me when doing computer science: It's a set of numbers, such that their order matters. Me when doing abstract linear algebra: Vectors are whatever I want them to be.

[@ivansantos1891]

That's exactly what I thought when I had classes of Linear Algebra 😂

[@CharlesPanigeo]

Lol right. Vectors are members of a vector space. Whats a vector space? Well its a space of things we call vectors.

[@ivansantos1891]

@@CharlesPanigeo "vector space" is basically the most abstract thing i've ever learned in math. "Learned" because after it the things become more difficult

[@CharlesPanigeo]

@@ivansantos1891 I've found thats how it is for a lot of people. In my undergraduate linear algebra class the majority of students were either CS or engineering students. They said the same thing you said about vector spaces being the most abstract thing they've learned. I had the same experience until I took an abstract algebra course later in my degree. Now I'm working on my masters in mathematics and my thoughts have changed. Abstract is a relative term. What was once very abstract is now easily understood. What I'm learning now seems abstract, but down the road i will probably think they are very concrete.

[@ivansantos1891]

@@CharlesPanigeo interesting

[@BenAHowell754]

What's our vector victor? We have clearance, Clarence. Roger, Roger.

[@ViliamVadocz]

Doesn't make sense since Clarence was asking Victor for the vector and then said said Roger to some other Roger.

[@BenAHowell754]

Surely, you can't be serious?

[@Nahuman]

I think he was being facetious. And don't call him Shirley.

[@123JimmyTheCookie]

My favourite film ever

[@ViliamVadocz]

Of course not.

[@hannahl3456]

His voice is so soothing........ I have no idea why

[@frankschneider6156]

+Hannah Leanne because you turned the sound off ?

[@owenloh9300]

agree

[@bobross3356]

I know right? I think he's the grammar guy from Khan Academy. I'm not sure

[@VIDEOEPPO]

I was just going to type the same but you had commented already. If only this guy was my professor, i would never have flunked!!!

[@zennologyofeverything7265]

I hate voice Fry tbh....

[@jacksonsay37]

Q: what do you get when you cross a mosquito with a mountain climber? A: nothing. You can't cross a vector with a scalar.

[@ThatControlUser]

Heh

[@clover4135]

wimpykidfan37 I don’t get it

[@ngoctramle253]

Ace Spade you will get there someday.

[@GamingKing-jo9py]

@@clover4135 mosquitos carry malaria so they are a malaria vector. Scaling also means climbing. And with you can't do the cross product with math vectors and scalars

[@vivianaxxr]

best intellectual joke ever

[@PandaBeatsStudios]

I thought Vector was a villain in Despicable Me. I'VE BEEN LIED TO

[@736Jar]

no no no! that's the thing, there were no lies, he says he was named after the mathematical term!!!!!! watch his intro scene "because i'm committing crimes with both DIRECTION and MAGNITUDE....OH YEAHHHHH"

[@hijack69]

I knew someone would make this comments

[@glitchingsky58]

Irving Washington is this an r/whoosh?

[@-hitman-9103]

Krystal_ Lillypøp read the last phrase

[@kokomrade2541]

The video: *YOU JUST GOT VECTORED*

[@shrug1250]

“Vector, because I’m committing crime, with direction, and magnitude!”

[@paolarocha5992]

OH YEEAAHHHH

[@sharonsmith4324]

OHHHHH YEAH

[@sudhirchaudhary6512]

OH YEAH

[@azure.6874]

OOOOHHHHHH ʸᵉᵃʰ

[@SuperBhavanishankar]

⁰⁰⁰⁰H Y3AH!

[@kumquats2842]

it's amazing how I learned this yesterday in physics and now there is a video on it. this isn't the first time it's happened lol

[@badatphilosophy]

I remember learning about eddy currents in physics class one day, and that very same day after I got home and was watching youtube videos, I came across someone with the username eddycurrents. legit

[@spacepopeXIV]

+Zayden Blaze It's weird how the world works

[@gamergirl3031]

U have V's picture Do u like BTS? Cuz I love them 😘💖💖💖

[@shruggzdastr8-facedclown]

kumquats: Could it have anything to do with you being tiny citrus fruits, or is that completely coincidental?

[@user-sy2vd3kn2x]

Its because youtube monitors your cellphone's mic

[@kwokydow2]

I like to pretend I understand these

[@payelsutar3208]

LiterALLY🤣

[@ziyadduraid4763]

😂😂😂😂me too bro So don't worry u9

[@toriningen4792]

these words sounds very complicated

[@shubhankardasgupta4777]

@@MAC-vi7fy nope, in high secondary... don't be a jackass.

[@hidgik]

Me too# Movement of inertia.

[@ThePattersonPod]

If you’re watching this in high school… actually pay attention in your math classes. I’m about to graduate college, and I have to return to studying things like this because it actually has use.

[@safinaxo5940]

I was told I wouldn't need math in college, until calculus hit me like a freight train and now here I am learning 11th grade maths and physics from the internet.

[@chichobar1705]

@@safinaxo5940 God...

[@safinaxo5940]

@@chichobar1705 if you're still in high school, take your science classes very seriously. Trust me you're gonna be grateful you did.

[@youssefxfadel]

Already knew vectors and scalars. But tensor, that's new

[@atharvpathak9062]

@Doomblaze- By the way, moment of inertia is also a tensor

[@_veselin_5048]

Pls tell me whats a Vector2 vector3

[@loop5720]

@@ahmadihameed6098 lmao

[@Iamtwohundredtwentyfive]

@@ahmadihameed6098 lol precise but not accurate

[@mastershooter64]

*A tensor is a mathematical object that transforms like a tensor*

[@DREMajed]

we need more mathematics video people ! please make more !

[@clipit4503]

use khan academy totally free and educative!

[@ganeshprasad9851]

@@clipit4503 dude that's 3 years ago! What a bummer :(

[@colleen9493]

@@ganeshprasad9851 lol

[@isibanidevelopmentpartners5824]

Yeah that's true.

[@slowcoding]

When I learned the vector in the high school and the college, I never understood why I should learn it. Now I do understand. I wish somebody at the school should have explained this way. Thank you, David for your excellent lecture.

[@dontwastetimeyouarelosingr8172]

Just learn it you will understand in future classes

[@Inquisite1031]

Funny thing is the video didn't even mention the most use case of vectors, which is to represent numbers of dimensions higher than 1

[@dank2635]

This is very straightforward, easy to understand and practical. Thank you for the explanation.

[@Accudio]

Although I loved the idea, I think the way vectors was explained was not particularly clear to those unfamiliar with them, but too simple for those familiar. Especially with the complex, unnecessary section on array and vector transformations which just complicate introducing and explaining what one is, I don't feel your "What is a vector?" video really did a good job on answering the question. However, from Tensors onwards I felt was very well done and interesting, and it's a shame the first section was not the same.

[@HermanToMath]

Totally agree with you!

[@slkjvlkfsvnlsdfhgdght5447]

I completely disagree

[@trolloftime5340]

@@HermanToMath hello 阿 sir

[@AhsenJabbar]

really needed this right now! you guys are doing a really really great job can't express how good these videos are.....keep up the good work

[@BenAHowell754]

Surely, you must be trolling

[@kenzaelfellah]

+Major Kong I actually learnt this at school and he probably did too so why would he troll? This really helps for a test paper

[@AhsenJabbar]

I'm talking generally.... like the whole organization is doing a great job... not this particular one

[@AhsenJabbar]

+Kenza Elfellah yeah... and whenever i have a test and they have a video on that, i just watch that video and that's it...I'm totally prepared for the test...

[@kenzaelfellah]

+Ahsen Jabbar yup👍

[@lolsflint7598]

"I COMMIT CRIMES WITH BOTH DIRECTION AND MAGNITUDE... OH YEAH!" - The REAL Vector.

[@athan13590]

They're the same vector?

[@luckingk2537]

Best animation I've ever seen, from a design pov.

[@egonics2068]

Thank you for posting this just after I had my Physics test.

[@pchebbi]

Precise, Crisp! Beautiful narrations! Thank you!

[@PouyaAtaei]

I wonder if this was the best short tutorial I've watched. Deeply grateful.

[@ShauriePvs]

the most awesome explanation i have seen on vectors! thank you TED

[@babatulani6361]

tfw this video dropped right when we started discussing this in school

[@SiddharthKarunakaran]

You ever heard of coincidence, yrjosmiel73?

[@babatulani6361]

Siddharth Karunakaran exactly.

[@leonardoreyes8235]

+Siddharth Karunakaran Or a conspiracy?!

[@babatulani6361]

I Have A Blank Face EXACTLY

[@SiddharthKarunakaran]

What is TFW?

[@bluu5345]

I thought a vector was a type of criminal partnered with direction and magnitude, but this video really opened up my eyes to the astounding reality of vectors! Thank you once again TED-Ed! 😌

[@lunaindustrys2601]

Having done game design before I must say this is well done. Would have loved to see you illustrate 3d vector math. But for now this is satisfying.

[@mustu4619]

Thank you. You explained vectors better than my physics teacher.

[@seppa340]

Great! I love almost every TED-Ed video.

[@olympiasnowstorm6254]

almost? lol

[@quangtoki8377]

+Olympia Snowstorm look at his profile picture

[@olympiasnowstorm6254]

Project Yisus XD

[@seppa340]

What's wrong with it?

[@ayusharora2019]

One of the finest explanations, that I had till now.

[@yisroel5556]

Thanks for explaining this. It makes it so much more simple. God bless you.

[@LLL_14_85]

As a science student, vectors for me were just on board or notebook, but never visualised as this much extent... Thank you for opening a new dimension of thinking

[@user-ck9bd2lh6f]

очень красивое объяснение, спасибо!

[@dfiori3]

YES PLEASE MAKE MORE VIDEOS LIKE THIS THIS EXPLAINED VECTORS SO WELL!!!

[@farefouse]

Video did a good job at explaining some properties of vectors. It needed to go over the direction of vector thing and how they can be broken down into single dimensional quantities.

[@jtamallari6778]

i really like this narrator

[@lioness9039]

Kindly see this video examination in life never give up -kzbin.info/www/bejne/oWXaZaOXoJtpjJI

[@MathCuriousity]

I still don’t understand how those are the same vectors.

[@luukstokhof5727]

Beautiful to see again after having used this for school

[@TDH12]

My thougths: What does it mean? It means Accelerator is fujcking smart af!! (Kudos to anyone who knows the reference!)

[@kazzfuchsia1073]

Me. I heard about vectors from that anime.

[@anzeg-]

Yoroshiku

[@humidsnake1291]

New season dropped

[@berry.x9388]

Indeed he was! His strength doesn't come from power alone. If he wasn't smart enough to do all the calculations needed he wouldn't be called the strongest in Academy City!

[@kiwoxgen9929]

I thought that dude just throwing stuff & able to levitate That's it

[@ArcaneFuror]

taught me more in 4:40s than my teacher did in 4.4 weeks!

[@krkaasyap8132]

this context and style is entirely different from your teachers' try to understand what to say rather than simply typing a youtube comment

[@abdelazizmetali1938]

whats a 4.4 weeks

[@masterofalltrades_]

Arcane Furor Then you surely have learnt more than just knowing what a vector is.

[@Melecie]

also, what did 4:22 onward teach you just wanna know

[@kabirulhassan3228]

o yeah... u r right

[@vchavez09]

So concisely yet eloquently explained

[@mcmac8027]

his voice helped me stay interested in any topic discussed

[@davidflores909]

This brings back to me a question that I've had for quite a while. Once I was trying to code a plane which each pixel would have a vector value and these would spread out at some percent in "time" so that it would be able to simulate waves. However, before I started too do any coding, I came across a really confusing scenario. If you have two waves coming in opposite directions which consequently annihilate each other towards the middle of the plane, I would expect them to continue after colliding, but it wouldn't be the case. All the information each pixel would have as data is the direction and momentum, but as these two opposing waves collide they would essentially wipe clean all data rendering impossible for the waves to go past each other as it happens in the real world. All I can think of to overcome this issue is creating a new instance of a plane for each new circular wave generated but this wouldn't be neither efficient nor practical.

[@horsecurse]

This is late but one of the way I could think of would be to transfer there momentum according to their mass and velocity in an elastic collision.

[@davidflores909]

@@horsecurse dang I did not even remember I had asked this. Yeah, you're in the right direction, but I think here it'd be more convenient to track the properties of discrete points in the plane. What I was describing was basically a tensor field. A tensor can hold on information about the "elasticity" and momentum of the field. Thank you for reminding me of this though. I never coded a tensor field, and I'm now curious if I can make it through with what I now know.

[@themasstermwahahahah]

Vector, Direction and MAGNITUDE!

[@chiimumango3979]

OH YEAH!

[@___9370]

This is kind of thing i need People always teach topics related to scalar and vectors But they are never properly defined what exactly are they

[@OmnipotentPotato]

Wow. The due date for my research on vectors has *just* passed, and KZbin has decided to recommend this treasure trove of useful and relevant information to me *now* ?

[@astaghfirullahalzimastaghf3648]

Vector is the sum of : The real distance travelled in space by an object in a straight line which can be expressed By an x coordinate or y coordinate of the destination point, or the sum of those two, in which the starting point is the origin of the cartesian plane which is assumed to be (0,0). The total distance travelled by that object cannot have intrinsic values because x coordinate cannot explicitly add y coordinate because their values might be different from each other. So, vector or denoted as "v" can be expressed by v=[x] [y] in two-dimensional array. Or, v=xi + yj ; Note that x value cannot be added explicitly to y value. The equation is just some sort of expression, not intrinsic addition. As for the vector magnitude, it is actually the displacement of the distance travelled by that object from origin to endpoint of the destination, in which can also be expressed as the hypotenuse of a right angle triangle with the x coordinate as the adjacent side, while y coordinate as the opposite side. As for unit vector, ^v = v/|v| This means, to get x and y coordinate of the unit vector with its magnitude as 1. I.e, the hypotenuse of coordinate x and y has the intrinsic value of 1.

[@MathCuriousity]

It took me 45 min to figure out why the vectors and how the vectors could possibly be the same considering clearly going In opposite directions. Can you tell me if my epiphany was correct;? It was this: The only way these can possibly be the same vectors is from the perspective of a being that itself is moving from the origin: if a person/perspective moves up to right 3 or left 2 down 3, from their perspective they still moved the same amount relative to the “center” origin! Did I do a good epiphany!???

[@megabrean]

Hi, i'm a physics student, i loved the description of vector, but i still struggle with the tensor, i know it's a matrix, but i would love to connect each term to their physical meaning, can someone point me a lesson that does that?

[@domenicoferrari5246]

I passed physics exam 1 month ago, I would have loved to see this video before, very easy to understand!

[@maskedmarvyl4774]

I wish we had this explanation available when I was a kid. Our teachers didn't have the tools to convey the information. And by tools I means the intelligence or the creativity required to convey it.

[@mastershooter64]

Mathematicians: A vector is an element of a vector space, if you can't understand it, then git gud skrub

[@nestoons4539]

It’s a mathematical term. A quantity represented by an arrow with both direction and magnitude.

[@kailashkirthy9882]

dude u like ..made my day !!! got a test 2mrw on vectors and this video just helped me soo much ! ;)

[@paulhaso]

Wow. Couldn't be better explained, thank you!

[@audreymarconuqui6263]

it feels so good to be able to understand this even before watching UwU

[@SuperBhavanishankar]

UwU

[@stephenjackson5065]

For the rest of my life I will always know the definition of a vector solely from Despicable Me

[@arredon2]

Thanks!!! I was very confused by tensors and your easy explanation throw some light into it

[@drona311]

The person taught me something not a single teacher could teach me in years (why and exactly the vectors are useful that is!)

[@narutoroxanne22]

Vectors are the reason Accelerator is the number one 5th level esper...!

[@AcZe1188]

and also the reason why he got beated by a level 0

[@narutoroxanne22]

Ac Ze naaaaa THAT level 0 has a special power that works against him bro ...

[@AcZe1188]

That guy is a special snowflake. He ain't give a shit about accelerator's stats

[@kkamau5479]

the only other person to almost become level 6

[@el7284]

Literally the only interesting thing about that series

[@monikagoyal7227]

Ted ed : 🙏🏻🙏🏻🙏🏻 My teachers : scalar ;only magnitude Vector; magnitude+ direction

[@OdysseyWorks]

This is brilliantly explained!

[@thomasbroome9307]

I needed this for my upcoming test thank you!

[@metalslug97]

I didn't understand vectors until 2 and a half years into engineering at university. 🤷‍♂️

[@stevennicol1659]

Ngl this kinda makes me wanna become the most powerful esper in academy city

[@gemmi1563]

is this a 'a certain scientific railgun' reference lol

[@janikaalday5026]

I honestly love the animation...it's so simple

[@renzojeripalomino4885]

I love this channel because of the book reviews they make, but I did not knew they would teach me physics, ¡cool!

[@theweirdcreeper3033]

Matrices next pls !

[@vitorentediado950]

helll yeeeeeeah ++

[@frankschneider6156]

+TheWeirdCreeper Hey, they already gave you an array, that technically a 1-dim matrix. The rest is just trivial extrapolation

[@---777---]

+1

[@guillemgarcia3630]

+Frank Schneider huh, trivial for you! (nah jk)

[@legendariersgaming]

Look up 3Blue1Brown's "Essence of Linear Algebra"

[@keyonthompson950]

I just started A certain magical index and I'm here to fully understand Accelerators power

[@couldyoubetender3480]

Im missing this in school right now because I had to do something and it really helps me......thank you so much

[@Plan36c]

Thank you. I love these light bulb moments. The language comparison was perfect.

[@theyoungknight.3119]

I wonder if Accelerator uses videos like these to keep a good understanding of his powers😂

[@ReeCocho]

Can we get a video on quaternions?

[@aka5]

This

[@EmperorZelos]

vectors + scalar = quaternions

[@aka5]

***** u sure m8

[@EmperorZelos]

Akașșș Yes, the concept of vectors comes from Quaternions

[@aka5]

***** Huh ok. Still doesn't really explain it, a vid would be very nice

[@haah3151]

good video is very good to know the functions of vectors and to help us and show us the correct terms

[@p199a]

this video is soo good i had problem understending tensors and i need them for simple physic game THX

[@naygoats955]

When you realise that a whole field of physics is an index reference

[@MathCuriousity]

It took me 45 min to figure out why the vectors and how the vectors could possibly be the same considering clearly going In opposite directions. Can you tell me if my epiphany was correct;? It was this: The only way these can possibly be the same vectors is from the perspective of a being that itself is moving from the origin: if a person/perspective moves up to right 3 or left 2 down 3, from their perspective they still moved the same amount relative to the “center” origin! Did I do a good epiphany!???

[@chikipichi5280]

Anyone here for accelerator

[@jerrylin7221]

Me

[@zyleb536]

Me lmao

[@chikipichi5280]

@@zyleb536 xd

[@thatoneguy4504]

Me too

[@sambhu4295]

I wish I had seen this video a year before , it might helped me in understanding physics more better...

[@djjdjd470]

Excellent!!! Our teachers directly started with properties!!

[@niaschimnoski882]

Unrelated, but: Why doesn't KZbin have an ×4 button?

[@sanankanwar6372]

I think thats pretty related lmao

[@chanuthgunawardene7579]

Yes go mathematics!!!

[@Anonymous_489]

Such an amazing explanation thanks❤!

[@starplayzreadbio373]

No one gon talk about the cool animation at the end of the whirls and how clearly it was illustrated?

[@barryhughes9764]

I'm afraid that this explanation is as clear as mud.

[@EmperorZelos]

I cry watching this as a mathematician

[@needpit1]

but are the tears from happiness or sadness?

[@TrostCrecy]

Why ?

[@95t95t95t]

I am with you mate... no talking about vector spaces is a shame. Treating vector like pointers...

[@giannisniper96]

every time a vector is treated like a set of coordinates, a differential geometer dies

[@EmperorZelos]

Trost Because htis is not how a mathematician views vectors, especially not an algebraist like myself

[@ngocnguyenn4512]

- I've learnt about this for several months. I can solve many exercises in Math about vectors. But not until today do I know what are they =))))))))))))))) Thank you guys so much. Pls do more videos like this

[@rizalpurnawan3796]

This is good, it tells from the basic using physical perception, which means many people would easily understand rather than if it is described abstractly. Like mathematics class used to do.

[@connieeko]

You're a year late with this video. RIP calculus

[@josephfox9221]

isnt this algerbra?

[@Thegamemakur]

Vector calculus.

[@josephfox9221]

Warden didn't know that was a thing...

[@SiddharthKarunakaran]

I don't understand this comment. What happened 1 year back that caused calculus to die now?

[@cheesecakelasagna]

Siddharth Karunakaran his calculus grades died probably?

[@FortWoodlockMedia]

Ted-ed: Physicist, air traffic controllers, and video game developers all have one thing in common... Me: They're nerds?

[@feelingspecial4345]

I feel so smart understanding it hehe I actually was just learning it and was about to write a note on this topic.

[@learnenglisheasily8578]

Thank you so much , finally I got precise idea about vectors

[@cgkty5315]

When ted ex make a video of what your studying in school

[@SuperBhavanishankar]

❤️🙏ikr

[@shashanklaur507]

Why is pressure not a vector quantity?

[@hammad8707]

Because pressure does not have a specific direction.

[@BigDoener]

because pressure p is defined as Force per Area -> p=F/A At least that's how we see it in physics.

[@95t95t95t]

Considering force is a vector one might thing pressure is a vector too. But the direction of the force, caused by a pressure (difference) is determined by the orientation of the area the force is acting on. The force is obviously always perpendicular to the area. Therefore F=p n A with force vector F, area A (skalar) and vector n (unit vector normal to the area)

[@prabalacharya4526]

Actually, pressure at a point on plane surface is defined as the magnitude of normal component of force acting per unit area around the point. It doesn't follow laws of vector addition i.e., parallelogram law of vector addition or triangle law of vector addition or polygon law of vector addition.In physics, when we talk about pressure , we mean magnitude of fore acting per unit area. It doesn't require extra piece of information to be known i.e., direction. Since a physical quantity pressure is expressed in terms of magnitude only, we can conclude that it's a scalar quantity.

[@MathCuriousity]

It took me 45 min to figure out why the vectors and how the vectors could possibly be the same considering clearly going In opposite directions. Can you tell me if my epiphany was correct;? It was this: The only way these can possibly be the same vectors is from the perspective of a being that itself is moving from the origin: if a person/perspective moves up to right 3 or left 2 down 3, from their perspective they still moved the same amount relative to the “center” origin! Did I do a good epiphany!???

[@nusantaranbrony7283]

thanks ted ed,this is more helpful than my online class

[@ahadabbas9567]

Thank you TED-ed I understood all about what vectors are.

[@dhanarsantika]

0:38 : vectors also have a magnitude, and an extra piece of information. Directions Linear Algebra : Am I a joke to you?

[@uhRoid]

This is grade 9 math

[@daltonysme8955]

Yeah but most people have forgotten it

[@sandeepdhariwal963]

Explained perfectly thanks for the video

[@manashbehera961]

Thank u so much for explaining this so clearly

[@apoolplayer278]

0:40 das a scary hairline

[@miles_8228]

No no no you got it all wrong its a villain stopping gru

[@jubayer355]

😂

[@indiragooda410]

His smooth voice.. And explanation 👏...

[@mauisstepsis5524]

Hands down the best tended video ever.

[@alking1307]

anyone will know this if you are at 6 grade

[@frankschneider6156]

+At King Tensors in 6th grade ? Seems like you made it to 5th grade at best

[@deleted1665]

how many years you have in the 6th grade? i'm not from USA

[@splattru]

I had this in kindergarten. bro.

[@ishalhuds4902]

I'm learn it from my mother at 3 years old bro!

[@geekyvors2837]

+Huda Isal i invented this shizz bro... and i wasn't even alive back then