Its like when you have full interest on what teacher teaching and you listen to it carefully you understands everything clearly and thinks that teacher is the best creature ever👼
@@mohammedadil7170no. Schools just pick the topic do it for a bit and move on to the next. To really understand it we need to do more selfstudy and practice stuff like questions. Schools doesn't have time to do all this and cover the entire syllabi, at least the way they go now. It's up to us. Also it's also depending on the teacher. Some teachers really have a way to make students understand thing by making sense out of things.
Dot Product or the Inner Product between two vectors yields a scalar. Cross product x X y yields another vector....one orthogonal to the plane shared by x and y.
Thanks very much. Didn't get the dot product for so long, and in one video you gave it to me in such an nice and easy way to understand. Very helpfull. Wish I had you as a teacher in school ha
woa that arrow analogy for the cross product going into or out of the page is awesome. I wish i had had that when i was first being taught about current and magnetism and whatnotz.
geometric algebra interpretation is much, much better. (a b) = (a . b) + (a ^ b) = |a||b|cos[theta] + i * |a||b|sin[theta] .... the cross product is a bad interpretation of wedge product.... (a ^ b) = i (a x b), where the cross-product obscures the fact that ordinary multiplication is related to complex exponentials.
Hey Sal, at minute 1:04 you say that order does not matter when you multiply two vectors together in a dot product. I Know we get the same magnitude, but wouldn't the direction run in the opposite direction.
Order doesn't matter with the dot product, because all you do is multiply corresponding components, and then add them. Ax*Bx + Ay*By + Az*Bz is exactly the same as Bx*Ax + By*Ay + Bz*Az. There are no non-commutative processes in the dot product. The cross product by contrast, is where order matters. A cross B = negative B cross A.
Are you starting with an assumption that we are talking vectors? I thought dot product was like this: I walk a mile in an hour, how many miles can I walk in 3 hours? Scaler times a "thing" of some kind (dot product, a quantity). Cross product: basic electricity, V=IR. Suddenly two "things" are being multiplied together (current and resistence). Commonly, vector abstraction comes later. Isn't that the essential weirdness of reality, the cross product, emergence of a new "quality"?
Dot product = a product of two vectors and a measure of how aligned they are. Cross product = a product of two vectors, a measure of how crossed they are, expressed as a vector that is perpendicular to both of the original vectors.
around 7:00 it was a bit confusing cause in the sketch it seems like you are drawling a line perpendicular to b, not a (the little orthogonality square was hard to notice) and I said to myself "wait that is not possible, how didn't he notice THAT mistake?" heheh :)
A force = 4.85 Ni - 7.36 Nj acts at a location = 3.99 mi + 2.21 mj on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?
if a (b)sin(angle) is the component of b perpendicular to a, then it should not necessarily be perpendicular to b. then Why do we say that it is perpendicular to both a and b
![[LIVE] : ONE ลุมพินี 91 | คู่เอก "คมอาวุธ vs อเล็กเซย์"](http://i.ytimg.com/vi/V0RkEfYFsgM/mqdefault.jpg)
shout out to you for being a better teacher than... well.. my teachers
Best comment reward 👑
Its like when you have full interest on what teacher teaching and you listen to it carefully you understands everything clearly and thinks that teacher is the best creature ever👼
best comment reward 👑
Omg, sorry to hear that. I tbought this one sucked
@@mohammedadil7170no. Schools just pick the topic do it for a bit and move on to the next. To really understand it we need to do more selfstudy and practice stuff like questions. Schools doesn't have time to do all this and cover the entire syllabi, at least the way they go now. It's up to us. Also it's also depending on the teacher. Some teachers really have a way to make students understand thing by making sense out of things.
I was amazed with the drawing xD
Yeah me to
ikr!
Lmao
was looking for this comment haha
You are a mathematician as well as an artist. Well explained.
Dot Vs. Cross Product: Top 10 Anime Battles.
Literally Mannn.... 15 years ago!!!.. I was just 2 year old back than!.. Amazing.!!
ikrrr
very funny, light hearted and informative. perfect!
I came here just for the awesome fingers
2:00 theta looks like ^_^
hahaha
ThX! sal
Excellent! very intuitive. You have a clear way of explaining things. Thanks for the video.
Dot Product or the Inner Product between two vectors yields a scalar. Cross product x X y yields another vector....one orthogonal to the plane shared by x and y.
ur not only a good mathematician, but ur also a great artist! the hand!!
Thanks very much. Didn't get the dot product for so long, and in one video you gave it to me in such an nice and easy way to understand. Very helpfull. Wish I had you as a teacher in school ha
You sir are my hero. I wish my Calc teacher spoke with the same clarity and english composition as your video.
Lovely hand drawing. fingers took the heart away ❤️❤️
This video was released when I was born and still the best explanation video of this topic!
thank you so much!! I managed to get an A1 in my exams just bcos of you :)
i have been learning art i can tell you that that hand is good, also you explained well, very well done.
😆 Theta in 2:00 be like. 😆
good drawing for the hand ..m
You are my God!
8:59 indian genes took over for a second there
what
If i am watching a 15 year old lecture video at middle of a night, it means the value he provides is soo deep. Thank you ❤
2:01 SM--> SMILE :D nicee
I was reading this topic for more than one hour , but ur video gave me hope !
Thank you so much KhnAcademy. These are great sources!
Just found myself teo useful channels one khan academy and the other one's yours
Calm mind... excellent concept
Thanks, this answers a lot of about cross products!
That's good drawing right there damn
|a||b|sin() can be seen as the surface area of the parallelogram formed by the vectors "a" and "b".
woa that arrow analogy for the cross product going into or out of the page is awesome. I wish i had had that when i was first being taught about current and magnetism and whatnotz.
Thank KA my professor doesn’t even teach you are a life savor 🙏
you are good at explaining .
now its time to upgrade and explain through animation
Thank you very much sir
16 years later and still better than my teachers.
Thank you. It is really helpful for self studying.
:) I agree.
Khan is so cool! *draw a masterful rendering of hands, wait 30 seconds, ERASE!!*
great video! helped a lot!
i wish u would be my home tutor who is a ocean of knowledge
13 years in the future, love you
Awesome youtube channel. Subbed and thanks.
one more thing ,can u please do a video on hydrocarbons-preparation of alkanes ,alkenes........etc.pleaseeeeeeeeeeeeeeeee
Is it only me who thinks soo or is Sal obsessed with the word intuition 😂
wow, very helpful!
Did not expect him to be such a goated artist out of nowhere wow
He draws better hands on a computer than I do on paper. Gosh
This tutorial will only make sense to those who already know how it works.
Storytale He already made separate videos on both the dot and cross product so maybe watch them instead of criticising him for trying to help people
This video saved me. Thanks!
Tomorrow is my exam and i am watching it now 😳
8:50 mind blown
Thanks for the great video :) great for general revision
I was 1 month old when this video had posted 😂 ooh my God really thanks
geometric algebra interpretation is much, much better. (a b) = (a . b) + (a ^ b) = |a||b|cos[theta] + i * |a||b|sin[theta] .... the cross product is a bad interpretation of wedge product.... (a ^ b) = i (a x b), where the cross-product obscures the fact that ordinary multiplication is related to complex exponentials.
Super! Thanks, Anneke
Thank's❣❣❣❣❣❣
Wow, that was ridiculously helpful. Thank you.
WOW this was posted literally in the same year as I was born.
fantastic explanation
Good job with the hand drawing
Thanks sir
mashalla thanks allot brother.....
I love this guy's voice! What's his namee!!??
Hey Sal, at minute 1:04 you say that order does not matter when you multiply two vectors together in a dot product. I Know we get the same magnitude, but wouldn't the direction run in the opposite direction.
Order doesn't matter with the dot product, because all you do is multiply corresponding components, and then add them. Ax*Bx + Ay*By + Az*Bz is exactly the same as Bx*Ax + By*Ay + Bz*Az. There are no non-commutative processes in the dot product.
The cross product by contrast, is where order matters. A cross B = negative B cross A.
Good video to share among the student
Should have mentioned the relationship and reason why sine or cosine is used in dot or cross product.
Simple and nice :) but the determinant way is better for understanding and tidy xD
Thank u man 💙
I've got to stop looking at these videos, I really should be finishing my homework.
Are you starting with an assumption that we are talking vectors? I thought dot product was like this: I walk a mile in an hour, how many miles can I walk in 3 hours? Scaler times a "thing" of some kind (dot product, a quantity). Cross product: basic electricity, V=IR. Suddenly two "things" are being multiplied together (current and resistence). Commonly, vector abstraction comes later. Isn't that the essential weirdness of reality, the cross product, emergence of a new "quality"?
nice, thank you
I waited for my physics prof to say what the cross and dot products meant practically.
That was a mistake.
Dot product = a product of two vectors and a measure of how aligned they are.
Cross product = a product of two vectors, a measure of how crossed they are, expressed as a vector that is perpendicular to both of the original vectors.
thank you!!
Aah 240p we meet again😀
'Hey Khanacademy! Sal here. Where are your fingers?'
Wow great
around 7:00 it was a bit confusing cause in the sketch it seems like you are drawling a line perpendicular to b, not a (the little orthogonality square was hard to notice) and I said to myself "wait that is not possible, how didn't he notice THAT mistake?" heheh :)
thanks
I request Khan academy to teach on white or black board
3:11 test
do a tutorial for hand drawings lol :) :D
Nice fingers
Very nice. You can teach this to a 6 year old child and it will understand.
Nice!
hey friends...plz tell me how r my videos
What do ladders have to do with this?
well explained, thank you very much!
Not gonna lie, that first angle was cute as hell.
A force = 4.85 Ni - 7.36 Nj acts at a location = 3.99 mi + 2.21 mj on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?
2
good
happy theta at 2:00
At 2:02 the theta looks like a laughing smiley.
easy way to remember (helped me)
dot is grayscale
cross is colored
In my school the fee is so high but the way they teach is so unworthy for that money they teach 😭
The sin Theta is going crazy 😜... Had laugh alot in 12 years........
I think I broke my finger. At least I can’t take the test now!
commenting from the yr 2024, nice video!!
anyone here in 2019?
me
So is it collinear or not
Is the first letter always the index finger?
if a (b)sin(angle) is the component of b perpendicular to a, then it should not necessarily be perpendicular to b. then Why do we say that it is perpendicular to both a and b
How do I find the sin of a smiley face?
Just ask Jesus for the sin list
Shout out II-BS Math A PSU Lingayen Campus...😅