What is a vector? - David Huynh
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- Опубликовано: 26 дек 2024
- View full lesson: ed.ted.com/less...
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.
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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.
That's exactly what I thought when I had classes of Linear Algebra 😂
Lol right. Vectors are members of a vector space. Whats a vector space? Well its a space of things we call vectors.
@@CharlesPanigeo "vector space" is basically the most abstract thing i've ever learned in math. "Learned" because after it the things become more difficult
@@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.
@@CharlesPanigeo interesting
His voice is so soothing........ I have no idea why
+Hannah Leanne
because you turned the sound off ?
agree
I know right? I think he's the grammar guy from Khan Academy. I'm not sure
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!!!
I hate voice Fry tbh....
What's our vector victor?
We have clearance, Clarence.
Roger, Roger.
Doesn't make sense since Clarence was asking Victor for the vector and then said said Roger to some other Roger.
Surely, you can't be serious?
I think he was being facetious. And don't call him Shirley.
My favourite film ever
Of course not.
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.
Heh
wimpykidfan37 I don’t get it
Ace Spade you will get there someday.
@@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
best intellectual joke ever
“Vector, because I’m committing crime, with direction, and magnitude!”
OH YEEAAHHHH
OHHHHH YEAH
OH YEAH
OOOOHHHHHH ʸᵉᵃʰ
⁰⁰⁰⁰H Y3AH!
we need more mathematics video people ! please make more !
use khan academy totally free and educative!
@@clipit4503 dude that's 3 years ago!
What a bummer :(
@@ganeshprasad9851 lol
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
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
+Zayden Blaze It's weird how the world works
U have V's picture
Do u like BTS? Cuz I love them 😘💖💖💖
kumquats: Could it have anything to do with you being tiny citrus fruits, or is that completely coincidental?
Its because youtube monitors your cellphone's mic
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.
Just learn it you will understand in future classes
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
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
Surely, you must be trolling
+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
I'm talking generally.... like the whole organization is doing a great job... not this particular one
+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...
+Ahsen Jabbar yup👍
I thought Vector was a villain in Despicable Me.
I'VE BEEN LIED TO
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"
I knew someone would make this comments
Irving Washington is this an r/whoosh?
Krystal_ Lillypøp read the last phrase
The video: *YOU JUST GOT VECTORED*
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.
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.
@@safinaxo5940 God...
@@chichobar1705 if you're still in high school, take your science classes very seriously. Trust me you're gonna be grateful you did.
I'm an post graduate who is watching 😢... don't underestimate the math and science class fellows
I like to pretend I understand these
LiterALLY🤣
😂😂😂😂me too bro So don't worry u9
these words sounds very complicated
@@MAC-vi7fy nope, in high secondary... don't be a jackass.
Me too# Movement of inertia.
Thank you for posting this just after I had my Physics test.
Best animation I've ever seen, from a design pov.
Already knew vectors and scalars. But tensor, that's new
@Doomblaze- By the way, moment of inertia is also a tensor
Pls tell me whats a Vector2 vector3
@@Shadow0.0001 lmao
@@Shadow0.0001 lol precise but not accurate
*A tensor is a mathematical object that transforms like a tensor*
This is very straightforward, easy to understand and practical. Thank you for the explanation.
"I COMMIT CRIMES WITH BOTH DIRECTION AND MAGNITUDE... OH YEAH!" - The REAL Vector.
They're the same vector?
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.
Totally agree with you!
I completely disagree
@@HermanToMath hello 阿 sir
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! 😌
omg vast difference in learning something and learning something from a good teacher. Very well done!
tfw this video dropped right when we started discussing this in school
You ever heard of coincidence, yrjosmiel73?
Siddharth Karunakaran
exactly.
+Siddharth Karunakaran Or a conspiracy?!
I Have A Blank Face
EXACTLY
What is TFW?
I wonder if this was the best short tutorial I've watched. Deeply grateful.
the most awesome explanation i have seen on vectors! thank you TED
Wow. The due date for my research on vectors has *just* passed, and RUclips has decided to recommend this treasure trove of useful and relevant information to me *now* ?
Vector, Direction and MAGNITUDE!
OH YEAH!
Ted-Ed videos just never fails to explain seemingly complex concepts beautifully. That's why we always finish the video feeling in awe. 👏🏻👏🏻
i really like this narrator
Kindly see this video examination in life never give up -ruclips.net/video/k4w4pak66V0/видео.html
Man you have my salute cause not only I understood everything but I was amazed by seeing this dynamic animation keep up
Great! I love almost every TED-Ed video.
almost? lol
+Olympia Snowstorm look at his profile picture
Project Yisus XD
What's wrong with it?
No one gon talk about the cool animation at the end of the whirls and how clearly it was illustrated?
Thank you.
You explained vectors better than my physics teacher.
The person taught me something not a single teacher could teach me in years (why and exactly the vectors are useful that is!)
taught me more in 4:40s than my teacher did in 4.4 weeks!
this context and style is entirely different from your teachers'
try to understand what to say rather than simply typing a youtube comment
whats a 4.4 weeks
Arcane Furor Then you surely have learnt more than just knowing what a vector is.
also, what did 4:22 onward teach you just wanna know
o yeah... u r right
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
My thougths: What does it mean? It means Accelerator is fujcking smart af!! (Kudos to anyone who knows the reference!)
Me. I heard about vectors from that anime.
Yoroshiku
New season dropped
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!
I thought that dude just throwing stuff & able to levitate
That's it
Beautiful to see again after having used this for school
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
3:34 “Even if you have forces acting in the same direction with the same magnitude depending on how they’re oriented you might see waves or whirls when force a vector is combined with another vector we have the physical quantity called stress which is an example of a second order tensor.”
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.
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!???
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.
I just started A certain magical index and I'm here to fully understand Accelerators power
Thank you. I love these light bulb moments. The language comparison was perfect.
I still don’t understand how those are the same vectors.
My life is literally vectors. Every class I'm in in college right now is all about vectors. From calc 3 to statics it's all vectors. And now this!
+Elijah Perez
Statistics ? Where the hell should vectors pop up in statistics ?
Frank Schneider Statics. not statistics. Statics is the study of material stress and forces that dont cause acceleration(aka net force is zero). But yes, statistics has no vectors.
+Elijah Perez what are you studying?
Method775 Mechanical Engineering
Elijah Perez
Yeah, my bad.
Mathematicians: A vector is an element of a vector space, if you can't understand it, then git gud skrub
I took pride by understanding these kinds of videos
This is how education should be
Excellent!!! Our teachers directly started with properties!!
For the rest of my life I will always know the definition of a vector solely from Despicable Me
his voice helped me stay interested in any topic discussed
Ted ed : 🙏🏻🙏🏻🙏🏻
My teachers : scalar ;only magnitude
Vector; magnitude+ direction
These Videos never Get OLD
Matrices next pls !
helll yeeeeeeah ++
+TheWeirdCreeper
Hey, they already gave you an array, that technically a 1-dim matrix. The rest is just trivial extrapolation
+1
+Frank Schneider huh, trivial for you! (nah jk)
Look up 3Blue1Brown's "Essence of Linear Algebra"
- 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
It’s a mathematical term. A quantity represented by an arrow with both direction and magnitude.
I didn't understand any of that, but what a nice voice.
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.
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.
@@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.
очень красивое объяснение, спасибо!
His smooth voice.. And explanation 👏...
Vectors are the reason Accelerator is the number one 5th level esper...!
and also the reason why he got beated by a level 0
Ac Ze naaaaa THAT level 0 has a special power that works against him bro ...
That guy is a special snowflake. He ain't give a shit about accelerator's stats
the only other person to almost become level 6
Literally the only interesting thing about that series
Im missing this in school right now because I had to do something and it really helps me......thank you so much
it feels so good to be able to understand this even before watching UwU
UwU
Hands down the best tended video ever.
I'm afraid that this explanation is as clear as mud.
Precise, Crisp! Beautiful narrations! Thank you!
I didn't understand vectors until 2 and a half years into engineering at university. 🤷♂️
One of the finest explanations, that I had till now.
Ngl this kinda makes me wanna become the most powerful esper in academy city
is this a 'a certain scientific railgun' reference lol
Vectors are vital! Thanks from India 🇮🇳 #TedEd
I wonder if Accelerator uses videos like these to keep a good understanding of his powers😂
Epic, first time that i got chills after watching a math video.
Can we get a video on quaternions?
This
vectors + scalar = quaternions
***** u sure m8
Akașșș Yes, the concept of vectors comes from Quaternions
***** Huh ok. Still doesn't really explain it, a vid would be very nice
Okay I'm a student of BS Math..... And he teached it very well.. 👍🏻
When you realise that a whole field of physics is an index reference
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!???
Thanks for explaining this. It makes it so much more simple. God bless you.
I cry watching this as a mathematician
but are the tears from happiness or sadness?
Why ?
I am with you mate... no talking about vector spaces is a shame. Treating vector like pointers...
every time a vector is treated like a set of coordinates, a differential geometer dies
Trost Because htis is not how a mathematician views vectors, especially not an algebraist like myself
thanks ted ed,this is more helpful than my online class
You're a year late with this video. RIP calculus
isnt this algerbra?
Vector calculus.
Warden didn't know that was a thing...
I don't understand this comment. What happened 1 year back that caused calculus to die now?
Siddharth Karunakaran his calculus grades died probably?
always in awe with the animation
Anyone here for accelerator
Me
Me lmao
@@zyleb536 xd
Me too
Just in time for eleventh grade physics. Thanks TedEd
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?
This video is such an amazing and a senseble
Unrelated, but:
Why doesn't RUclips have an ×4 button?
I think thats pretty related lmao
BEST EXPLANATION SO FAR *-*-*-*-*-*
the only thing i learned from this video is that dog in spanish is perro
I love this narrators voice so much
Yes go mathematics!!!
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.
Ted-ed: Physicist, air traffic controllers, and video game developers all have one thing in common...
Me: They're nerds?
Thank you TED-ed I understood all about what vectors are.
Why is pressure not a vector quantity?
Because pressure does not have a specific direction.
because pressure p is defined as Force per Area -> p=F/A
At least that's how we see it in physics.
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)
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.
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!???
I passed physics exam 1 month ago, I would have loved to see this video before, very easy to understand!
When ted ex make a video of what your studying in school
❤️🙏ikr
wow hundreds of video explanations out there in one video . Thanks
No no no you got it all wrong its a villain stopping gru
😂
That language analogy is amazing
0:38 : vectors also have a magnitude, and an extra piece of information. Directions
Linear Algebra : Am I a joke to you?
I honestly love the animation...it's so simple
here for best boy accel
Who's that?