The dot product | Magnetic forces, magnetic fields, and Faraday's law | Physics | Khan Academy
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- เผยแพร่เมื่อ 3 ต.ค. 2024
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Introduction to the vector dot product. Created by Sal Khan.
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One simple mistake. Relax. This guy is a boss.
+Zachary Boeder Cosine starts from 1 at 0 degrees, and it decreases from 1 to 0 until it reaches 90 degrees starting from 0 degrees. If one already has the 3 values of cos30, cos45, and cos60 in his memory, then he should be able to know that the smallest of those 3 values belongs to the highest degree of the 3 degrees, and that the biggest value belongs to the smallest degree. To decide whether a mistake is a small or a big one, you should take into consideration the cause of the mistake. Hopefully that makes sense.
I'm gonna mention cos 60 is 1/2 so I can feel better about myself too.
Yes. And this teacher writes the "6" like a "b" which is very annoying for a kid.
@@mikel4879 and he should get a real job.
(btw, these are all jokes we actually appreciate him, I feel the need to explain it to reduce the potential anxiety in the world)
Pleasure 🤍
I love how he says, i dont know what to call this at 2:40 , ( But he obviosly knows its called the projection, because hes a boss), and then he shouts out, lets just "randomly" call this: " THE PROJECTION OF A ONTO B!". Jesus, thats a good name for that thing you just came up with ;) .
Sal great video! Just two small corrections. cos(60) = 0.5, also the block won't slide horizontally, it will actually get lifted up in the air, because 100sin(60) > 10. Thanks for the video though!
I like to think of it as "The combined effort of both vectors". Khan Academy is a blessing!
Can you help me please?
I dont understand why we multiply instead of adding Bcos(theta) with vector A
Cos60 is 1/2!!
+chaitanya ingale xd xd xd xdx xd xd xd xd xd xdx dxd xd xd xd xd dx xdxd xd
+chaitanya ingale he meant in radians... cos(pi/3)=cos(60)=1/2
+chaitanya ingale Glad to know I am not the only one that makes irritating mistakes, and he is a teacher.
+Said Zaid-Alkailani yea but cos pi/3 is still 1/2
sin 60° is √3/2
Thank you so much! You never fail to explain something in a way that makes sense!
cos60=1/2. but that's the charm of Sal. here's a brilliant mathematical mind that still makes simple mistakes from time to time like the rest of us. for people where math does not coming naturally, that's comforting.
big shoutout to a youtube channel for teaching me more about calculus that my professor with a doctorates in math
THANK YOU SOO MUCH for the lecture. neither my book or my instructor proved this in the class so I was sooo confused. you cleared it all up for me . Thanks!
I am a IIT-JEE Aspirant and I was confused so badly that what is actually a dot-product, you cleared my doubt thank you !, It is 18:40 21 December 2022 !!
Thanks ! now I can die peacefullly
you run out of oxygen tomorrow, right ?
Finally understand the point of learning dot product now. Let the celebration begin!!!
This cleared up so much for me. Thank you!
so when you say projection a onto b switch of the two is the subscript, the b i'm guessing?
I know it's been 10 years today since the video was posted but I just wanted to make sure that he knows that Cos60=1/2
In case he didn't get it from the other 238 comments about it. ;)
at 2:40 it is called as vertex/tip of the angle
Look at how the magnetic field works. I'm almost positive that the magnetic force is the cross product of an object's velocity vector and the magnetic field vector.
Best Dot product explanation!
@WhutsWhat let me tell you think about a triangle. you can calculate the length of it if you know the angles, (with cosine theorem..)
am i right then let me move on now i want you to decrease one angle of the triangle. i want you to make that angle as 0' ok?
now you have a line. am i right , ok now use the cosine theorem. lets call lengt of that line as ''a'' and the length of a point will be ''x''
x.x = a.a + a.a - 2 .cos0.a.a
x.x = (a - a) . (a - a) this is a simple explanation
@Elzelgator So what exactly is your argument here then? I agree that every line made by atoms has a lot of space between them but what does that have to do with anything on this video?
Great Video. Clear and concise.
Thank you so much. Well taught!
You are great, sir.
The dot product of force (one vector) and distance (another vector) gave a scalar which was work. If I were to ask what physically would be the resultant vector in a cross product (what sort of vector in physical terms if the first two vectors were force and distance) could someone offer a few suggestions?
This makes so much sense now!!!
messy but great info. thanks.
can you please do a video in interpolation and quaternions?
Thank you for nice information sir
He would have failed that test question. :(
THANK YOU SO MUCH FOR RELATING THIS TO PHYSICS! I understand physics very well but in math I have been so lost the past few days! Now I have a new way of seeing it! THANK YOU!!!!
Ryan Kochan -_- why didnt you automatically relate it to physics? PHYSICS FOR THE WIN BOYS
the antilogic vector is a part of maths as well :p
shreyash tiwari
what? how does math ≠ math? he is trying to think of DOT PRODUCT not vector, it has to change his thinking, just because they both have the same term doesnt mean they are the same. That is not thinking in physics (conversion)
@Ryan Agree.🔷
Thank you🙏🙏🙏 sir
good ol' crunchy 2008 videos
Thank you for explaining logically which make sense and thats why khan academy is different from all other channels.Thank you ☺️
@@slips5815 was pretty clear to me. i didnt know anything about dot product and i could easily follow this video. he explained the intuitive part good as well. seems like a skill issue
No 2/10 content
10/10 skill issue
@@six-zx7qw -8/10 Profile Picture :)
Skill issue? That comment was so long ago I’m into Analysis at this point man -_-
"Big and fat" lmao!!!
i knew i wasn't the only1 XD
**necros ancient comment epic style**
I like em big, I like em chunky
I was searching for this type of intuituve video from past 2 days, finally found what I was looking for.. thanks bro..
Hi there I am a science teacher and I am expanding my background and certifications to physics. This has been an amazing review! Thank you so much for these videos
Stick to heroin Lou
Great explation
But everyone complain cos60=1/2
Hello khan
you are amazing
Cosine of 60 degrees is 1.2, not (√3)/2
Could anybody tell me how vector b times cos theta should be b in the same direction as a
Did your village just get the internet? It is fun to type profanities to strangers for a few decades, but eventually you will find other uses for it.
I wish you were my professor
@TDAWizard Yes, thats y his answer was off.
Just amazing. i liked how you applied it to physics. :)
how come you don't have a video on 3d coordinate systems?
Sal, kau memang terbaik!! (google translate it =D )
14yrs before uploaded
and quality of video is still amazing
cos(60 degrees) = 0.5
he performed few mistake in many 400+videos
Sir cosine of 60 is 1/2
cos60=1/2
Nice presentation. However it will be nice to call displacement vector instead of distance.Also please tell me what happens when i have two vectors both are velocity vectors. Will the dot product of two velocity vectors will be a scaler quantity ?
Harish
ohhhh so thats what this is used for? cross product is easier in my opinion but to each their own.
Nice explanation.... thanks. :)
vectors kind of hard but wil get there
Vectors themselves aren't hard. Operations on them are just ridiculously abstract.
Thank you!
And for all you kids who think you'll never need this knowledge in the "real world" -- I do right now and I'm 33. Wish I'd paid more attention in high school. :)
@WhutsWhat you missed the best part! he wants to help and be amazing for FREE!!!!!!!!!!!
Thank you sir, I truly appreciate the effort you've put into these videos.
You're making my revision alot easier!
Amazing how these topics are never taught with such simplicity I'm college or high schools. It seems like teachers were always just saying this is the dot product am this is how to do it. I becomes dirt easy when when it can be broken down into what it really means.
oops what a blunder - supposed cos 30 is sq3 / 2; cos 60 is .5
Check ur calculator, it won't lie.
Not a huge mistake. Just divide the result by the square root of three. No biggie.
True about the TONS of topics, but in most he never really derives anything from first principles. For example, the dot product video above, he begins with the geometric definition of the dot product and then attempts to explain it. Of course, almost no one derives anything from first principles, so perhaps I am hold Khan to too high a standard.
However, I appreciate that the videos are available. But I usually show my students other videos.
@WhutsWhat you have to be kidding me... do you think this is good teaching lol...let me tell you something. in our country thre is lot better teachers... and they are in every school. and also lot of theacher wait for some to employe them... what ever...
and also with my teachers ability i found a formul to find out length of a point.
if you want me tell it ican tell it to you and everyone in your school can envy you...
reply it if you want me to tell you
Yeah I know it..Doesnt matter your opinion true or not..When you make a negative comment to a video that get more like than dislikes, It is obvious that the comment get to many dislikes...
However we all humans.. So we always try to show our opinions to others.. To make them interest with us..
I am another weak human.. so..
Textbooks are not made for people who don't know the subject (the typical student) and teachers are not hired to teach, they are hired to do research. ON the high-school and community college level, it's lack of imagination, laziness or plain incompetence on the part of teachers.
Lol.. Instead of arguing with me listen to him XD.. You will gain much more thing..
I dont care which argument will gain more "like" XD
I need to do better things.. You all strange.. Why even give try to reply my comment..
It was just a opinion.. Lol go and study it will give you more thing
He certainly isnt a normal man because he has exceptionally good teaching skills. If you understood english better you would realize just how intuitive he can make the most abstract sounding concepts. You've got your head up your arse because this man helps millions, and its all not for profit...
Roger, Roger. What's our vector, Victor?
GREAT WORK I CANNOT SURVIVE MY COLLEGE YEARS WITHOUT YOU GUYS KEEP IT UP
I can't remember exactly who said this, but a wise person once said: A moron explains the simplest things in the most complicated way; a genius explains the most complex things in the simplest way. Khan is a genius!
Isnt cos60=0.5 ?
I had a feeling people were going to head straight to the comments just to correct him.
yall got some nerve in here giving Sal advice and bad mouthin. I know his teaching methods are effective because they have really helped me. keep it up my boy, you're Great
No worries kiddo. Im not trying to bash you either, but did you not expect to get shut down by hordes of people for questioning the brilliance of our great sal?
@Elzelgator a point doesn't have length, it is defined as an infinitely small area in space. So go tell your teacher to go back to 6th grade geometry.
@tkatiqah yet, you understand the theories behind each steps. this is what calculus all about, math is not all about calculation, is more about theory
sin60=3^(.5)/2 and cos60=1/2
Just a tiny slip of the tongue from our boy, Sal.
Don't tell him or he will divide by zero and all hell will break loose.
but why do most books simply state ||F|| * ||AB||? how did the cos theta disappear and where and why? theta can't be zero for cos theta to be equal to 1 ain't so?
when he’s actually lifting that 10N box off the ground
in what situation the scientist gone to think about dot product?what is the nessecity of dot product?what is the inspiration behind this?
I have just understood that :
The scalar product is not useful thing , Why?
Because we already know that :
1. W= F . d
2.The projection of F on d is = F.cos(theta) x d
So , what is new in this process?!
I wonder, why the box is not lifting up from the ground, therefore, change the angle. then change the net force .... ermmm....
With all due respect, have you seen the sum of his videos? And it doesn't hurt to know the school from where he graduated.
just an advice should have had that vector pulling the cube be pointing towards the ice so that the cube will be lifted
cos(60) = 1/2
Best teacher. Thanks
cos (60) = 0.5 man
anywayz thanks alot
I think cos 60 is 1/2 but the rest of the vedio is great
Could you please sir tell me about
Why we take dot product between acceleration and magnetic field ???
And also reply me acceleration . Magnetic field is equal to what is??
Sal, I think you should, maybe, cheat a little and keep your trigonometric ratios cheat sheet near you when recording. You should not look to us like a mere mortal or else you'll lose your "math god" status. Just pulling your chain! Great little nugget! --with errors.
cos 60 is 1/2.
100 N would pull the object off the table. The vertical component 100 sin60 is greater than 10N.
he is a not a genious. in turkey we all learn this in the highschool lol he is a normal man lol..
Thank you so much. I finally fricking understand this concept. Reading the book is confusing at first
I cant believe that noone argued with him about tht cos 60 part but accepting it, alarmingly it shows tht most of the audience are here for his sexy voice and not for physics
Adjacent of what to what? You seem to be complicating stuff instead of explaining
What about the projection of b onto a. Nobody every illustrates that. And how do you choose which?
Hey Sal you videos are very helpful, but in this video you said and use the COS for 60 degrees is the square root of 3/2. The COS of 60 degrees is actually 1/2. Thanks again