The dot product | Magnetic forces, magnetic fields, and Faraday's law | Physics | Khan Academy
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- Опубликовано: 7 авг 2008
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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 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
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!
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!
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 ;) .
I'm with natlustifus, now that I understand this, this is easily the coolest thing I've discovered all weekend. I've always been trouble with the intuition behind sin, cos, and tan, and I thought I wouldn't be able to learn this because it dealt with cos. But it's all picture clear now. I'm learning to learn this and the cross product to understand how they apply to curl in a vector field.
This cleared up so much for me. Thank you!
Thank you sir, I truly appreciate the effort you've put into these videos.
You're making my revision alot easier!
Really helpful tutorial. I can't believe I finally understand. I can't thank you enough. Thank you.
GREAT WORK I CANNOT SURVIVE MY COLLEGE YEARS WITHOUT YOU GUYS KEEP IT UP
Thank you, your're better than my lecturer. Really surprised you could explain in 10 min and I can understand.
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.🔷
Very helpful. Thank you, Sal!
Thank you sir for posting these videos u actually explain the how and the why you actually give ppl intuition into what they are doing not simply saying here memorize this and youll be good like most teachers now a days for that i am very grateful.
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!
its very clear! specially the projection concept. Thanks a lot!
Cool! The explanation why using cosθ is super clear.
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.
Very helpful! Thanks!!
This makes so much sense now!!!
Thank you so much. Well taught!
It's understood perfectly .nyc job !
Thanks for the wonderful suggestion. It seems very impressive! A few more suggestions? Seems very interesting. Thanks very much!
it is the first time i get the importance of dot product " physically " , not just signs and numbers , thanks "Sal" :)
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
Awesome! I am very thankful!
14yrs before uploaded
and quality of video is still amazing
Thank you so much. I finally fricking understand this concept. Reading the book is confusing at first
messy but great info. thanks.
so when you say projection a onto b switch of the two is the subscript, the b i'm guessing?
Best Dot product explanation!
Thanks ! now I can die peacefullly
you run out of oxygen tomorrow, right ?
Beautiful explanation as always :)
Thank you soooooooo much!!!!! it really helped
Nice explanation.... thanks. :)
Finally understand the point of learning dot product now. Let the celebration begin!!!
Great Video. Clear and concise.
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 !!
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 -_-
it realy helped me
thanks
His ability to teach amazes me.
good video for revision at the very last minute..
Great lecture!
Best teacher. Thanks
Could u pls do a video on the dot product in component form
Thanks was wondering why the formula for the dot product was like that.
Actually in Nova Scotia it isn't in our curriculum so when I left there for Uni elsewhere this was very helpful.
Give this man noble peace prize. What good explanation.
Thank you for nice information sir
great job
good use of colour.
i like to think that this guy made all of the videos in one day
Thank you!
Really wonderful
big shoutout to a youtube channel for teaching me more about calculus that my professor with a doctorates in math
Great video, thanks
You are great, sir.
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.
He is a genius!
dude, one word. leeeegendddd!!
thankz a lottt :)
nice tutorial
What about the projection of b onto a. Nobody every illustrates that. And how do you choose which?
How is this different to orthogonal projections?
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??
I dont want to argue with you. That wont give me anything..
But I am still saying he is just a normal man :)
It was really helpfull to me 1 year ago.. Thanks to him :)
His education and teaching level helped me so much..
Thats all :)
thanks for the vid.
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. :)
just an advice should have had that vector pulling the cube be pointing towards the ice so that the cube will be lifted
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. ;)
I dont know who are you but your videos are really helpfull, thanks for labour..
Could you fix the pixels? It's very hard to watch at the highest option of 240p
Could anybody tell me how vector b times cos theta should be b in the same direction as a
at 2:40 it is called as vertex/tip of the angle
can you please do a video in interpolation and quaternions?
why do you time the component of a in the direction of b by the length of b
Better than coaching classes cofortly sitting infront of pc and learning this holy stuff thanks alot M.R. G.E.N.I.U.S :)
very good
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
god bless you, sir
how come you don't have a video on 3d coordinate systems?
you are amazing
so he is greatest
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?
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
king of you tube! thanks
Thank you🙏🙏🙏 sir
The best angle must be equal to (tan inverse ( friction coefficient)) ..... for example if the friction coefficient = 0.6 then the angle is equal to 31 degree to minimize the required force :)
Just amazing. i liked how you applied it to physics. :)
Wondering about the other Definition of Dot Product, where U take the Components, multiply them, and then Sum them to also get a Scalar. How show they are Equivalent?🟦
Why we get cos theta for scalar product and sin theta for cross product????
I wish my teacher taught like this
good ol' crunchy 2008 videos
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...
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
There are two little problems with your example of the block on the ice. If the block weights 10N, and you pull on it with 100N at an angle of 60 degrees to the horizontal, the vertical component of that force is 100sin(60) or about 87N. So you're pulling up 87N on a box that is only held down by gravity by its weight of 10N, so the box would be quickly lifted off the ground and its displacement won't be horizontal.
Also, as many others have already pointed out, the cosine of 60 degrees is one half, so the horizontal component of the force is 50N and the work is 500J
D. (A. B) Does this equal anything ?! Or It couldn't multiply triple scalar product.
THANKS!!!!!!!!!!!!!!!!!!!
good video
in what situation the scientist gone to think about dot product?what is the nessecity of dot product?what is the inspiration behind this?