Visualizing vectors in 2 dimensions | Two-dimensional motion | Physics | Khan Academy

[@Peter_1986]

I love how Khan always gives you those "aha!" moments. ^_^

[@IBeExtraCool]

That 36.899 was messin with my ocd man. I felt like taking a Sharpie and writing on my screen that it's 36.8699 lol

[@johannaandres6207]

Watching this 10 yrs later :)

[@Changedman_70]

Still helpful after 13 years

[@pinkrink]

Think as vector quantities. He is moving up at a certain velocity (3m/s) and right at a certain velocity (4m/s). The distance is not 3+4, but the velocity is 3+4 because of the direction. Together, he is moving in the direction of ||a|| at 5m/s. It's hard to explain in text, but try to get your head around that :)

[@dominicochoa9925]

Because 3^2+4^2=5^2 9+16=25. Pythagorean theorem. Hopefully this helps someone a bit

[@MalikthaSneak]

Still helpful after 1000 years!

[@suprajhegde1405]

really helpful.but notice that angle made by the triangle is 36.8699.but in further calculations it is written as 36.899

[@sairuchir542]

yea your right

[@jimmynguyen9562]

yea i noticed the same thing

[@sairuchir542]

Same, but its alright humans are not perfect. By making mistakes they learn, so same with this thing.

[@yotamdubiner2545]

omg bro thats crazy

[@yotamdubiner2545]

@@sairuchir542 no

[@tophatsheep3747]

Hello mr Khan, you’re vídeos are amazing and incredibly helpful, the only bad thing I read the Spanish subtitles and at points in the video they stop showing. These videos are too good for me not to tell you this and would be cool from you to find the problem. That doesn’t take away that you’ve helped me and I appreciate it. Gracias 😁

[@namanrajsingh6139]

I wish, you would have been my teacher, Sal... Telling this thing from the soul of my heart...

[@ScorpiaX]

What I did in a 75 minute class could be summarized in Khan's 8 minute lessons. Thank you for helping people like me to understand better ^^ or at least an essential integral lesson without taking too much time

[@antacidd3981]

I love u so much Mr. Khan, I use khan academy to study physics everyday in summer, thank u !

[@FranklinaFlick]

Oh my gods, THANK YOU!!!! What a lifesaver of a video!!!!

[@irisakame]

you saved my life!

[@adityathadani7066]

I wish time travel was possible

[@adityathadani7066]

Guys, Guess what!!!

[@robertjohn2220]

Wow, the graphics have come along way, great work In the diagram he uses 36.8699 and in the calculations it changes to 36.899

[@theunahime7446]

It happens sometimes when we are doing things in a flow. It's simply just that 3,4,5 are Pythagorean triplets, sal has basically put in the exact degree angle necessary to make the sine and cosine ratios come around to give ||a|| sin © = 3 units for perpendicular and ||a|| cos © = 4 units for the base and the specific angle is © = 36.8699°. We all get careless. My dad used to purposely write a minor step wrong to check my attentiveness and correct me afterwards after comparing the solution with the book provided back answers and then make me get it corrected. Anybody with a scientific calculator or Google search can find the inverse of © = sin'(3/5) so it's not that big a deal, we got the concept rest is just knitpicking, which we should avoid. He's doing humanity a service, we should give him a break. But the visual software seems a whole lot more attractive by his way of using it. Thanks khan academy for the nice differential section.

[@youtubesam7591]

So clear to eyes.

[@mylove8951]

Excellent Math travel! give me knowledge, and just like a poetry makes me happy and feel good. I need this and I love this course, thanks for my teacher.

[@winterstellar]

This is my favourite hobby! To visualize vectors in two dimensions! Or even three!: )

[@hanashah1]

You are very good at explaining things..Thank you very much,you're a lifesaver 😁

[@glug307]

God loves you guys!

[@Hino_55]

Very clear explanation Sir Sal! Thankyou!!

[@muhammedshibin7008]

Very helpful 👍

[@tibg95]

sine and cosine laws.

[@ThePakhiLife]

3:39 Pythagorean’s theory

[@ibakedthecake]

pythag is for right triangles only

[@RidleyE]

you are a fantastic human being.

[@GuruprakashAcademy]

Excellent. Very informative and to the point.

[@TheExcalibur356]

What did u use to make this??

[@shayareedas8808]

thnx.a must watch for every student.

[@myleswebb1188]

Game changer! Ty

[@williamrobinson5859]

Thx bud

[@imanonce8105]

Thank you

[@user-noursameh]

A real life saver..thank you a lot!!!

[@louisrodriguez2739]

I think im color blind ! :P

[@zel_ni_kai_at_ken]

thank you so much :D

[@zkmalik]

awesome explanation..

[@damienwayne3755]

I LOVE YOU!!! I finally get it!

[@TU-qc5xr]

sal i could listen to your voice forever lol

[@milan1397]

i love how its explained like we're in kindergarten

[@JustAnotherYoutubChn]

@Phr3shBeatz dude it'll always make a right angle triangle

[@maycontainnuts3127]

i cant believe how poorly i was taught all this at school

[@spacedoutmars]

I’m a noob, how came vector a and b don’t equal c? Or does it?

[@sanjayshukla8666]

Best vdo ever

[@sudarshanchauhan5900]

Too gud I loved it

[@brendanmilton5025]

Hi, great tutorial! where can I get the calculator from?

[@islulison]

Thanks but you should help us with giving examples of word problems. This still helped alot though thank you very much.

[@2013dvan]

plus all the time in linear algebra

[@gerimujo3650]

thanks khan academy

[@MrShinobiguy]

it's cool since, the main purpose was to get it as close as possible to the whole number

[@edsknife]

All of the problems that we've been dealing with have stemmed from the fallibility of humanity.

[@frutfly]

you'e right my man

[@ahmedkhalid1167]

What is name the program that you use to make this video

[@karishnaryan9926]

*thanks alot*

[@Phr3shBeatz]

what do you do if its not a right angle triangle?

[@wendycorbett70]

Sal, you make things less complicated

[@eshanimhatre]

why does his voice sound like he has a cold ?? i like the video BTW

[@barryhughes9764]

Find the explanation of vectors confusing ! If any two vectors in R2 can be added anywhere in the plane then depending on their initial positions they can end up anywhere in the plane, is their final position in the plane irrelevant? If so why? Also I hear vectors described as being parallel and in the same direction......how can this be so? If two vectors are parallel then they cannot be in the same direction......they can have the " same orientation " but not the same direction. Example, if one vector points due North and another vector is parallel to this but offset say 500 miles then it is not in the same direction as the first. I only wish that definitions and illustrations of vectors was more rigorously approached and explained.

[@bftb1000]

Barry Hughes - It's a weird concept at first, but that's the case-- "direction" is referring only to the direction that the arrow end of the vector is pointing in, and it doesn't take into account its position in the coordinate plane. The direction of the vector is quantified with an angle (the angle the vector makes in relation to the positive x-axis). You can literally put the vectors anywhere on the plane and not change the vector itself, but it's handy to have them touching so you can see how they relate visually and use trig functions to find the component (horizontal and vertical) parts of the vector. So, vectors are a length (magnitude) and a direction (angle). Hope that helps!

[@barryhughes9764]

I appreciate the time you have taken to reply to my query. However it doesn't address the points I was making. I'm aware of the dot product , cross product, bi vectors etc. As I have said , and this is the pertinent point, vectors cannot be both parallel and in point in the same direction......they can however have the same "orientation".....so why leave the idea of " direction " open for interpretation? Also, one cannot say that the addition of say, two vectors in R2 or three vectors in R3 is independent of it's position. Surely the " force" or say the " acceleration" at one point would have a different effect on a system depending on " where " or it acts in the space of either of the above dimensions,........and these are the concepts I don't see being explained, specifically. Please, I intend no offence in this reply and am grateful for any clarification.

[@Ethan.J.C]

yea no one is perfect

[@IndranujChatterjee-is-a-ninja]

does he write all that with his mouse? i dont get how he does this

[@worldsbiggestholdthegirlfan]

+TheBinary There are tablets the connect to computers which have a stylus where people can write on those tablets and it can be transferred to notes. This is what my college professors use.

[@AeroeGraphix]

To add on he's probably in photoshop or something like it, and he just cut out the excess part of the screen so all we see is what he draws.

[@ForgottenBathory7]

Can sin and cos formulas be applied in every problem involving two vectors?

[@abdullahelnaggar7362]

yeah :)

[@ForgottenBathory7]

Thanks.:)

[@vijaynauhbar9424]

a train moving with acceleration of 5 m/s^2 have 1 engine of mass 100 kg and 4 coaches of mass 50 kg each find the force exerted by 3rd coach on 4th

[@plodazed61]

How can you solve this without a calculator, say on the CSET Math Subset 1?

[@yesname96]

did you get the answer? I also have the same question please lemme know the answer too if you already know!

[@Hyyacinth]

@@yesname96 its been 7 years i dont think he will answer haha

[@rymichael7203]

if vector X = Xy+Xx then how the hell does 5=4+3. this is what I don't understand about vectors. how is the resultant equal to the sum when pyth teaches us that c=the square root of a^2+b^2. I can not reconcile the two together. this should be the first thing explained so there is understanding.

[@noahgorman681]

For adding vectors, the components are not mathematically added to equal the resultant. It's merely conceptual.

[@gregorybancroft5990]

I think you might want to plan your videos more, so that it flows better. Also try not to repeat yourself when you right things down.

[@johnsmapreacher6525]

Despite all the KZbin videos I've watched so far I still don't understand what a vector is. Eventhough I know how to deal with the math prob, I still can't picture a vector in real life. The knowledge my guy is taking too long to get here...

[@Phr3shBeatz]

ahh kk. but do you know?

[@xoverlorderx]

virtual scientific calculator...wow @.@

[@mayko2468]

David Tran yeah it used to be fascinating 6 yrs ago lol

[@TheBhje]

hahahahahha noticed the mistake

[@rizwana547]

Plz Sir, try to explain basic things, for the sake of revision. Plz dont repeat the words more than 2 times. Thanks

[@vijaynauhbar9424]

pls help me

[@parthmaske3294]

1tip:Change background to white to improve quality of vid.

[@DogeFrom2014]

***** I guess khan knows that most of us pull all-nighters ;)

[@rojdaaahmd5480]

DOGE™

[@DogeFrom2014]

Rojdaa Ahmd Yes?

[@bushranaheed7531]

Black is better

[@BigBallaBarno]

Anyone here from mr andersons class, if u are there is no hope for u.