Everything You Need to Know About VECTORS

[@FloatyMonkey]

Please let me know what you think of this video and the series. Should my next video cover Trigonometry or shall we dive straight into How Games Work?

[@louise9757]

I would love the video about trigonometry! This video was so good 👌

[@joshuamora411]

Give us understanding of math while showing us the connections and crazy interactions in game makiiing

[@StoryTime_By_Arunlal]

Nice video man.

[@braytonmarumo215]

Your video offer a good start sir superb you are helping us

[@gutzimmumdo4910]

yes

[@cremebrulee2484]

I learned vectors in physics but not maths. I got the basic concept but not the notation so this clears it up nicely.

[@biscuit_6081]

awesome video!. I would just like to point a little error at 16:35, where it says sin(270*)=1, wherein it actually equals negative 1

[@CosmicComputer]

This was SPECTACULAR! Please, please continue with the trig intro in the next video! This is an outstanding resource and you’ve put a lot of care into this! Thank you! I think it would be really awesome to take some of these concepts straight into unity through code later in the series and see the practical implications as well. This is so good man!

[@FloatyMonkey]

Thanks man, I just started working on the Trigonometry video. The idea of translating some concepts into code sounds interesting to me. Could you give an example of how you see this in concrete terms?

[@CosmicComputer]

FloatyMonkey could be interesting to see, and I know unity has built in functions for a lot of this, but for like finding distance between a player and enemy for ex., or a grenade throw with a parabola etc. Just things of that nature, it would be in keeping with the more introductory nature as well. Really excited for the next video!

[@perryperry7257]

@@FloatyMonkey gg

[@kirangirija7567]

pretty precise and straight to point , makes a lot more easier to understand thank you

[@HopDubstep]

You're a fantastic teacher. I liked how you demonstrate a concept with care to the progression of thought as to what the next thing to think about should be that creates a "smooth" / natural unfolding of what it is. You remind me of Feynman in this way and It's great. This was easier than I expected for me to follow.

[@FloatyMonkey]

Thanks, and well that's quite the comparison! I put a lot of care into my videos, glad you found this one easy to follow.

[@dfinitial1885]

@@FloatyMonkey if someone compares you to Feynman You know you have done a good job

[@Rayneisprettycool]

Im watching this at 3 am instead of sleeping, thanks youtube recommendations Edit: why is this my most popular comment

[@bossbaby4194]

2am for me

[@abinlouis3747]

I'm sure you are preparing for neet or jee

[@avishkarandika4473]

you are not alone

[@omgshortvideos6156]

Hhh Amazing Am also see at night 3 Am 😘

[@teenva]

4 am 😔

[@pookstah]

I'm retaking last semester's math exam in two days and you helped me immensely by making me realize it's not as scary as I imagined and helped me actually understand how to do operations. Thank you so much! Definitely will be keeping an eye on your stuff.

[@PoweredUP_]

How was your exam?

[@compatetivepirate]

These vectors are very basics compared to Indian grade 11th science group for 15 year old kids 😢

[@geekypicky810]

​@@compatetivepirateshut up lil Indian, you learn the same thing as others but keep stupidly bragging about it 😂 That person is talking about their success and you gotta be a jerk as always lmao

[@zergling2621]

​@@compatetivepirateIndian scu m

[@user-vm3lz6ve6g]

@@compatetivepirate yes we get it, you guys are on a whole different level. sadly this drives a lot of the indian youth to commit suicide. the rigor from school plus high expectations from parents ruins you.

[@biscuit_6081]

bro this is SO GOOD. I had the brilliant idea of watching this video before taking the remaining exercises of vectors. you explained every concept so clearly. Thank you so much!!

[@cobywalker3922]

Finally a video that explains this without anything unnecessary and in an easy to understand fashion. Excellent video! Thanks so much for making it!

[@ali-faizyab]

This guy deserves more attention.... His way of explanation is very good 🥰

[@decreer4567]

Honestly this was the perfect video that helped me find the exact equations I was looking for in a robot I was building. I'll sub if you do a series on Linear algebra.

[@ABC-jq7ve]

The Passing Linear Algebra playlist is pretty good

[@D3lor34n]

Love your channel, not sure why i watch all these videos since i was originally only looking for a recap of rendering pipelines in general, but i enjoy your explanations even if i don't necessarily grasp every last bit from the get go. But i'm just some casual viewer mind you, well done in general!

[@FloatyMonkey]

Thanks, means a lot!

[@623-x7b]

For me the lack of music makes this much more enjoyable for education content this is a clean and easy learning format

[@beyza2000.]

You are my saviour! I was just watching NLP for ML course, and this came up, and I panicked since I didn't learn this at all at school during dropping early from school. U taught me everything perfectly, making it very easy to understand, and now I can continue my self study NLP journey! Thank you so much! My hero!

[@Der_Rotsteiner]

You really helped me, thanks .

[@kanvardeepbainsal9558]

great video, you went straight to the point and made it simple to understand :)

[@omaressam9380]

Amazing way to explain a topic like vectors. I am so grateful for your work. Thank you

[@annafedorchuk1178]

the fact that I didn't know anything about this before I watched this video and now I feel pretty familiar with this topic says a lot! You have a real talent for explaning things. Thank you!!!

[@saniyazahra555]

I didn't study physics in my matric and intermediate, but now I need to learn vectors for machine learning. This video doesn't give me the slightest vibe of a non-physics student. Hats off to you, sir.🙌🙌

[@jim2376]

"Do we have clearance, Clarence?" "Roger, Roger." "What's our vector, Victor?"

[@loveandthunder2928]

😂

[@ansumanc]

@Belgutei Uuganbayar how's this even funny lmao

[@jim2376]

@@ansumanc How are you such a sour jackwad, bozo? Have another sip of vinegar, loser.

[@ansumanc]

@@jim2376 triggered? Lmao

[@jim2376]

@@ansumanc triggered? humorless? Lmao

[@rabbitcreative]

2:50 I just got into an argument with a math-teacher (geometry) about exactly this. Sal of Khan Academy describes vectors using (x, y) notation, and something doesn't sit with me, telling me that a vector is direction + magnitude, and then using (x, y) to describe it. What you said-demonstrate from 2:50 - 2:59 is precisely what I want to see-hear. I want to see more of a lead-up to that though. Those 9-seconds I think should be like 30-seconds, or something, because what you did there is CRITICAL for language.

[@shrinkhalalala6808]

I can see why your teacher argued with you

[@rabbitcreative]

@@shrinkhalalala6808 > I can see why your teacher argued with you Care to elaborate or are you satisfied with dropping your sarcasm-turd and walking away?

[@Sammysapphira]

They are analogous but fundamentally different math concepts. It just happens that the notation is incredibly similar.

[@ShikharSrivastava-eo7fx]

It is THE BEST video for understanding vectors! It clearly explains the basics of the vectors! Wish I had seen this video earlier...

[@Angelo-vb6dg]

I was needing a refresher and this was absolutely great... you just earned a new sub.

[@futurenewton5303]

You got a new subscriber bro, In india we are never taught like this, Amazing animation along with your understandable explanation ❤

[@archykhn4513]

Everyone is taught like this only on KZbin mate

[@THEASPHALT9LEGEND]

hey, not only india, everywhere. the guy's right. I'm and indian and i'm in the uk, and you almost never even get taught like this around where i live.

[@THEASPHALT9LEGEND]

plus, the lessons are way better in america, some schools in india, rather than the schools in the uk.

[@THEASPHALT9LEGEND]

or in england a shall say...

[@THEASPHALT9LEGEND]

either way, it's your oppinion...

[@labforlife123]

hii :) i love your explanations, i was wondering if you could start a series on combinatorics and discrete maths as I feel like lots of people struggle to understand this

[@crazychicken8290]

what ur pfp

[@yagnikbose8973]

"Lucky for us, there has been a famous mathematician Pythagoras who made a formula for this..." As if we never heard of the man😂. Loved the video throughout man. Huge respect.

[@Devil-kz8ef]

Originally it was not given by him first, it's just westerns steals everything.

[@VictorOrdu]

This is an excellent and comprehensive presentation! Thanks 👍

[@slyzarrdmeme4803]

I’m already dreading watching a whole bunch of these videos to prepare for college physics, what was I doing when I signed up for that

[@t.gamer0410]

vi este video hace 2 años, no entendi casi nada, ahora lo volvi a ver y es una pasada de video. gracias

[@disciplechoi2685]

Geez... after scouring you tube for something to explain this to me, this video is ... P...e..r Perfect! Thank you @FloatyMonkey

[@chiennguyenngochoang2300]

I'm from Vietnam and this is a piece of art, thank you a lot FloatyMonkey.

[@flash_gif]

I'm glad I found your channel, keep up the awesome work!

[@TheExplainer989]

Vectors are mathematical entities used to represent quantities with both magnitude and direction. They play a crucial role in various fields, including physics, computer science, and engineering. Here's a brief overview: 1. **Definition:** A vector is often denoted as an ordered set of numbers, represented by an arrow. It has both magnitude (length) and direction. In 2D space, a vector might be written as \( \langle x, y angle \), and in 3D space as \( \langle x, y, z angle \). 2. **Components:** Vectors can be broken down into components along coordinate axes. For a 2D vector \( \langle x, y angle \), the components are \( x \) and \( y \). 3. **Magnitude:** The magnitude of a vector \( \mathbf{v} \) is denoted by \( |\mathbf{v}| \) or \( \|\mathbf{v}\| \) and represents its length. For a 2D vector \( \langle x, y angle \), the magnitude is given by \( \sqrt{x^2 + y^2} \). 4. **Direction:** Vectors have a direction, often measured as an angle with respect to a reference axis. 5. **Vector Operations:** - **Scalar Multiplication:** Multiply a vector by a scalar (a single number). - **Vector Addition:** Combine two vectors component-wise. - **Dot Product:** A scalar product that involves multiplying corresponding components and summing them up. - **Cross Product:** Applies to 3D vectors and results in a vector perpendicular to the plane of the original vectors. 6. **Applications:** - **Physics:** Used to represent forces, velocities, accelerations, etc. - **Computer Graphics:** Vectors represent points, directions, and transformations. - **Engineering:** Applied in structural analysis, fluid dynamics, and electrical circuits. 7. **Unit Vectors:** Vectors with a magnitude of 1 are called unit vectors. In 2D, the standard unit vectors are \( \mathbf{i} = \langle 1, 0 angle \) and \( \mathbf{j} = \langle 0, 1 angle \). Understanding vectors is essential for solving problems involving motion, forces, and various other physical phenomena.

[@ranielseanh.bautista5033]

This is such a cool video The way of teaching and the animations are way too smooth

[@leevivisuri8955]

- Very nice video with visualizations! One major problem I encountered though: You have correct answer about vector subtraction of a-b but the visualization is incorrect as we would end at the tip of vector -b NOT at the tip of vector a. - OK I GOT IT you are correct as the vector has the same magnitude and direction but the location of vectors doesn't matter so you decided to put it there. Exciting! Thank you.

[@ehe_6951]

KZbin recommended this to me when I finished my vector midterm exam last week and failed terribly (6/20)😭😭😭 I don’t understand why I need to learn this in 10th grade. But you’re a great teacher!

[@lalithavakada5541]

Rguktian?

[@ccmmenter]

In 18 minutes I understood more than after 7 and a half hours of lectures!

[@MuhammadGana-m7g]

this video is very comprehendable and everything was simplified

[@giancarlojRamos]

it would be nice if you make a full video with more details on each of the subtopics:) New subscriber here!

[@afbdndv8290]

I can't describe my gratitude. Thank you 🙏

[@AriiEDM]

so my teacher told us to learn about vector online because we will learn about it tomorrow and i just open you tube for fun and somehow this found this video haha lucky for me also thank you love the video

[@김재완-u1n]

This is the best lecture on vectors that I've ever heard! Why had my high school teacher given us the lectures so difficult? Hahaha. Over 23 years have passed since then. I miss the school days. Thank you for wonderful lecture.

[@hacksxor]

You have my respect, excellent video, explained perfectly.

[@calmmuffin4926]

this guy>>>>>>>>>>>>>> my liner algebra uni teacher

[@mr.rich3]

The best video KZbin ever recommended to me. Thank you sir.

[@yeabsiramekonnen6805]

tomorrow I have a maths competition test and you saved my ass! you deserve the SUBSCRIBE BUTTON!!!!

[@deadhorse7439]

best video explaining vectors I have seen on the internet keep up the videos

[@ashfaqhossain114]

Still helping students! Thank you so much for such a high quality video

[@RohitSharma-kg5ye]

Really good video with good animation, helped me in doing revision Thank You 😃😃

[@Mathematchit]

I've never understood what Vectors were let alone Matrices but i am insanely good at Analytical Geometry now, i am insanely good at all three

[@rickfuzzy]

Love your channel. Well explained and very useful

[@leamalki5859]

You explain things so well! Thank you :)

[@timeisapathwalkingtounderstand]

Thank you for making this video whoever you are. I appreciate it here in New York City listening watching and learning.

[@Musfiqur_anik]

this video would be massive helpful for a highschool student who is just starting their senior high studies .

[@TommasoP-of5tx]

I don't understand the cross product you can explain this?

[@dr.rahulgupta7573]

Excellent presentation in simple words.vow !

[@jb2_69]

Clear as heaven *should also add some non-essential on screen info like this while explaining

[@Rajesh_Chhetri_Shahu]

Thanks it helped me ... Lots of support and Love from Nepal

[@rohangayakwad2474]

Why don't you make more new great videos like this? you really help clear doubts in short time .

[@shmeef279]

actually such well made video, literally no bullshit and well put together and in a good order

[@SouthTC2]

Made it very simple to understand, and proved just how simple mathematics can be if you don't overblow what you're doing, good video, FloatyMonkey. You just expanded my knowledge in vectors

[@Rahiqalkotob]

me before exam:

[@RolandDamilola]

WOW I really enjoy this❤❤❤ Thanks you for taking your time for this

[@jackkrauser1763]

"in other words, you can think of the dot product as a measurement of how parallel two vectors are". Very well said

[@MuhammadYounasKhan-sr3oi]

Hello

[@devpro8214]

this channel's underrated and idk why his voice seems to be so familiar! Thanks for sharing your knowledge with us!! 😊😊

[@jennylimao]

Great video, hug from Brazil!

[@winexhd9373]

I think it is important to consider, perhaps a more abstract, but relevant point to make, to an introduction to vectors. I will start off with a joke. A mathematician, a computer scientist, and a physicist were hanging around in the cafeteria of their university. A student approaches the three and asks "What is a vector?". Surely, as masters of their fields, they can answer this seemingly basic question. The computer scientists speaks, "A vector is just a single columned matrix, like an array almost". The physicist smiles a little bit, perhaps with a touch of arrogance, and speaks, "You are partially correct but not completely, sure a vector can be represented as a matrix, but the original thing itself is an arrow". After much back and forth between the physicist and the computer scientist on what is the true essence of what a vector is, they turn to the mathematician for clarification. A mathematician says "Both of you are partially correct, but none of you are completely right". And then he walks away. I guess the point is that what does it mean for a thing to be something? Perhaps that is a deeper question from epistemology which I will try not to get into. A mathematician may suggest that a vector is anything that satisfies the "vector axioms" and operates "vector-ally". This seems like a circular definition so I will try to make it more clear. Any object, any thing, any concept, that can satisfy the vector axioms, is a vector. It may not have to have any physical significance, although to a physicist, it almost always does. But if a computer scientists wants to use vectors to represent non-physical such as the parameters of sensitivity of an AI model, then he may do that. In that case, an arrow may represent the AI's sensitivity vector, but it's physical representation serves more of a visual representation of a concept, rather than maybe being an actual thing.

[@jawaharbabuadapa]

Thank you for making these videos available

[@TMK264]

Oh my goodness! This was beautiful to watch! Please continue making more content! You teach beautifully!!!!! Thank You!

[@fahrenheit2101]

Straight to the point, but this glosses over a lot of things like the equivalence of the 2 forms of the dot product, and applications of the 2 products (beyond those that are essentially part of the definition). I guess it's still a godsend for people who don't have a clue what a vector is though.

[@AdebesinAdeolaTemitope-if1lb]

I just aced mathematics. Thanks so much. GODSPEED

[@jakov051]

I have an exam about vectors soon and this video was really helpfull, hopefully I pass! :)

[@mr.perfect7431]

You've explained it so efficiently a great video for vectors revision on last moment when u have no it idea abt vectors

[@Joseph-ex4sf]

Brilliant video, thank you! This really simplifies the concepts.

[@Naomi21435]

We learned this at 7th grade and still now we are learning 😢

[@gewaldro9478]

I just finished vectors and now the video is recommended to me. I wish I had found it sooner. Anyway thanks for the explanation

[@f1cti]

Very good explanation of the dot product!

[@rodlinjunior9446]

At 9:26 that Escalated quickly😂

[@Cellate]

13:26 for convention a = vector a, square root is ;/ and square is ^2 ||a|| = ;/a . a move square root to left side to make the magnitude a square ( ||a|| ) ^2 = a . a ||a|| . ||a|| = a . a what happened to the cos ?? well its a straight line since its only one vector so its cos 0 degree which is 1 Have a great day and continue your study :)

[@emillyskinner3780]

omggg thanks. this is super helpful

[@strongplatypus7663]

These visuals are the best and they help so much

[@alisaeidsharifi7910]

All the things that I need for machine learning 🙏 ❤

[@williamperry5767]

This gave me a brain explosion with solving vectors, I almost cried. Thank you

[@markmcsision-qb2sf]

solve this The graph shown on the grid square below is that of y=e^(-2x). Draw the graph of y=x+1 and x=2 on the same grid. Find the area bounded by y=e^(-2x),y=x+1,x=2, and find the y-axis.

[@Navyasandhya]

Thank You Sir❤🥳

[@HuzaifaMuhammadSIddique]

At 6:25 the resultant vector of a - b is wrong. It should be in the negative y-axis and positive x-axis because the coordinates are (3, -2)

[@FloatyMonkey]

It is correct, as explained at 1:43, it doesn't matter where we draw the vector since vectors are defined only by their direction and length.

[@HuzaifaMuhammadSIddique]

@@FloatyMonkey i get it. Thank you!

[@yoo_nishka5927]

This was really helpful as it makes your concepts crystal clear.. :)

[@richardbailey2001]

Love the animation because it makes the subject much easier to understand, but, I must admit I'm a little confused about the hand idea, because at 15.00 the (a ,s ) and ( b ,s ) don't line up with my hand.

[@Utopian1234]

I know this video is pretty old but I just feel obligated to let you have some serious talent for breaking things down and making them make sense with minimal effort on the part of the viewer

[@FloatyMonkey]

Thank you so much!

[@giorgossakkatos6101]

well, this was insanely helpful, amazing job.

[@yevsell]

This was very refreshing. Thank you.

[@junjun2541]

thank you, I was so confused about this, but now It's so clear

[@Mod3bola]

the best, also a very aesthetic video

[@gauravmggs]

Can you please explain Integration and Differentiation please 🙄

[@hectorescobar9450]

Do you have a practical use explanation, where we can use this knowledge to build or manipulate geometry in the viewport?

[@amjadsuli3540]

You’re an amazing teacher and thank you so much please keep making more videos

[@torukaa.8393]

Because ā•ā are in the same direction. Therefore 0(theater) = 0°. Cos 0° = 1. So ā•ā = a². √a² = a

[@SB-rf2ye]

For unit vector notation, you should use ihat, jhat, khat, not exhat, eyhat, ezhat. It's simpler.

[@gabislifestyle4514]

WOW! Thank you so much for your video. That was very helpful

[@vanessawertheim]

thank you so much! this is very helpful for my physics class :)