To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.
1) A very clear and understandable diagram 2) Great way of animation. 3) Awesome way of teaching. 4) A good mound of effort 5) Subtitles in all languages.. And much more!!! I can't just thank you enough. Thanks to help and guide...
Eugene, I don't think you'd ever expect to hear someone say this, but your videos have helped me fight depressive thoughts and anxiety. I was once caught in an deterministic perspective on the world and lived a life thinking my existence had little impact. Then I stumbled upon your quantum mechanics video and it gave me so much hope and wonder. I realized still have so much more to learn about this reality and that our very existence impacts the world around us. Your videos explain sciencific concepts incredibly well and make them so interesting you have actually made me consider taking up a career in physics. Thank you, I appreciate your work greatly. You have impacted my life and brought out the inner child in me.
+Aquas Studios, I am glad to hear that my videos have had such a profound influence on you. It is nice to know that my work is having a positive impact, and thanks for the feedback. To the best of our knowledge, according to quantum mechanics, it now appears that we do not live in a deterministic universe. I plan to soon have several more videos dealing with quantum mechanics, and I hope you will enjoy them too.
@@allankaige7364 It's been good, I went on to get my bachelor's of science in computer engineering. At the time I was a high schooler that was going through a little existential crisis.
extra: if the result of the cross product is 0 (null vector), you have two parallel vectors if the result of the dot product is 0, then you have two perpendicular vectors God Bless you all.
If you are wondering, the name of the song at the end is called William Tell Overture by Rossini. Please listen up the long one and not just the finale
It's the best thing when I am searching for an animation and find my way back to this channel :) They make everything so much easier to visualize and understand
Still dont get the idea behind the Dot and Cross product.. I'll just memorized the formula, then solve the problem, get an A+, never asked why, and go on with my life..
@@cinquine1 Same, I'm studying a degree in engineering and we're looking at the cross product between instantaneous angular velocity and perpendicular radius to find instantaneous linear velocity, and I have just realised are perpendicular to each other vectorially. So I guess I _do_ have to know about cross products after all! I was thinking to myself, "goddamit...." Although..I've now found out it makes the whole process sooo much easier to understand calculating this all _vectorially_ using numerical unit vectors rather than taking a geometrical approach using their magnitudes instead (lots of confusing lines and trigonometry :/ )...which is why nowadays I'm actually starting to appreciate cross products a lot more than I had done in the past. That's something I never thought I'd say cause I found them hellish to understand in further maths. But they're actually fairing out to be _extremely_ useful when finding perpendicular magnitudes that are in a three dimensional space with each other...such is the case with angular motion. You just have to know about this fact beforehand. All you have to do is arrange two perpendicular vectors in a matrix with their unit vectors above, and find the determinant of this, for a third vector that's perpendicular to both. After that I was wondering why tf I never did this in the past cause it was so straightforward compared to how I was doing it with trig... Saves time learning a bunch of different formulas when all you have to know is that (with unit vectors) : i = j *x* k ; j = k *x* i ; k = i *x* j ; and they are not commutative, so the reverse is the negative of those. Eureka moment for me XD (please tell me if I'm wrong about this :S )
You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: ua-cam.com/users/timedtext_video?v=h0NJK4mEIJU&ref=share You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.
Your other videos have been very explanatory. I like that they assume a novice viewer. Unfortunately I'm not following this one. It might help if you could detail some applications...like the time/speed/distance application in your calculus video, that made it clear how such a thing is used.
Hahahahhaha I cracked up so hard when the dramatic instrumental music came when revealing the cross product direction. Never thought such an informative thing would do that. Now I'll definitely replay that moment in my head during the exam.
This is a fantastic video! No waffle. Not too slow, not too quick. Just perfect. Thank you for these amazing videos. They help me visualise what the hell is going on underneath all those ridiculous maths problems I solve haha 😅
I have been doing dot products for years now, no professors have ever explained it this well, and I think visually, so because no professors explained it, in my head I always said it was "how much the vectors are of each other." But this video helped me understand so much more.
Another beautiful visualization! These videos should be used in college as well as in universities!! And, for totally unknown reasons, I would like to see a behind-the-scenes. Making videos like this must be a daunting task.
This is the absolute best video I've ever seen that defines the dot product. All of the conceptual stuff that other videos try to explain pales in comparison to the simplicity of this visualization.
this may be trivial to many, but to me, who only needs to remember crossproduct and dotproduct basics every 5 years or so, not doing vectors in that much detail usually using a blackbos, its easy to get your memories confused without such good visualization.
Don't stop you keep blowing my mind with simple stuff I have been using cross products for years and never realized it was just the area between the vectors
This was really helpful to visualize, but I'm still confused as to why multiplying 2 vectors results in a third one that forms a 90 degree angle from where the 2 vectors connect. Why does it happen?
This is what has been bugging me since i was introduced to vectors in school. This is my biggest lack of understanding in the fundamentals of physics. I have tried a lot but never found q clear explaination to this. So i have convinced myself that this rule is something that humans have agreed upon by conducting experimentation and finding results that just fit this type of calculation, and no one came up with it on thier own. While the dot product is very obvious and can be understood by doing your own thought experiments.
Imagine a cardboard attached to the base of the vector. The length of the vector would, therefore represent the area. The length even represents force in Newton, and other things, so the units don't have much to do with it, it's about the magnitude.
ok the question I always ask, what came first ? the cross and dot products or the physical phenomena that we needed to use these products for? for example, the work = force * distance ... did we need to come up with the dot product to describe this phenomenon (that the work should be scalar, and it cares about the force component thats only towards the motion vector) , OR, we already have the dot and cross products and we used the dot here because it applies ?? I HOPE I GET AN ANSWER ....
I just loved this video. I found the books to be too theoretical and never understood this concept until I watched this video. Definitely built my concept for lifetime. Thanks a lot 👏
When i heard the title of video i remembered the video about electromagnetism and gyroscope i guess :) Thanks eugene . Without you i would have stuck in physics very badly :)
im not certain the arrow for the dot product was right. i couldnt figure out how you got the length of the red arrow. from my understanding the dot product is one vector's projection onto another vector. i didnt quite see that. i gotta be missing something here.
With the dot product, the component of the slanted vector must be multiplied by the length of the other original vector. The above video seems to indicate that the dot product is just the component of the slanted vector.
This was so superb....at the end of the video I felt dots connecting in my brain and at the very same moment the music was playing in the background!!!
Thank you so much!!! I've been struggling to visualize the dot product and cross product for the longesttt time. This animation helped me so much! As well as the circuit video I saw the other day!
You know, in high school I've always dreamed about how great it'd be if there were people knowledgeable about physics who could also animate complex topics they were discussing because there are some things that are hard to visualize. Can you imagine how cool a physics and animation major would be? :) There's also a lack of animated physics videos, but here you are animating physics videos very well and fulfilling one of my dreams! :D I'm very proud of you and the work that you do, and I'm forever grateful. I wish you the best in your endeavors. :)
EDIT: oh it's just a scalar. got confused from so much amazing visual animation :P -isn't the dot product commutative? if it were then the resulting vector should be the same, but according to the animation it follows (is alligned with) only one of the original vectors (RED vector follows A not B). I understand the magnitude is the same, a.b.cosine, but the geometrical vector...? i'm confused-
You videos were awesome like unfolding mathematics in to a movie , it makes looking outside world in terms of math . I thank you so much for your videos ,love from india
Man, nice music selection like Rossini's William Tell Overture with a beautiful animation for a math explanation. You got an inmediate new suscriber in myself!
when considering the second arrow (segment on dot product) the length of that side of the triangle is simply the x component of the the second arrow vector.
I have just couple of weeks away for tensor calculus exam and have found this video very helpful , i would request you to upload videos on cross tensor product of tensors and tensor product of tensors if possible
To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available).
--To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable.
--To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video.
--If you believe that the translation in the subtitles can be improved, please send me an email.
I like your explanation 😉😁
I can't find gear symbols under this video
I love the terrifying climax of the music when they show the hand
it makes me scared of math
It's like they showed the ultimate universal secret. It's in the HAND!
NicksDomain101 Yup. Excellent but awkward.
Thanks, I spilled my drink laughing at your comment.
This music makes me feel like I am some Mathematicians thinking hard of a very tricky problem in 18th century.
Came for cross product, left with existential crisis.
Hahaha legend
RMSVideos oh god
Same bro, same
legend
Lol
This video has such an ominous energy and I was not prepared for it.
The music is like: Harry Potter and the Vectors calculations chamber.
XD
ROTFL
True
Ok
1) A very clear and understandable diagram
2) Great way of animation.
3) Awesome way of teaching.
4) A good mound of effort
5) Subtitles in all languages..
And much more!!!
I can't just thank you enough. Thanks to help and guide...
Thanks for the compliments.
Marco,
4) Amount of effort. Not mound of effort.
@@danielstewart3507 Yeah 😅
the ending song was perfect
Eugene, I don't think you'd ever expect to hear someone say this, but your videos have helped me fight depressive thoughts and anxiety. I was once caught in an deterministic perspective on the world and lived a life thinking my existence had little impact. Then I stumbled upon your quantum mechanics video and it gave me so much hope and wonder. I realized still have so much more to learn about this reality and that our very existence impacts the world around us. Your videos explain sciencific concepts incredibly well and make them so interesting you have actually made me consider taking up a career in physics. Thank you, I appreciate your work greatly. You have impacted my life and brought out the inner child in me.
+Aquas Studios, I am glad to hear that my videos have had such a profound influence on you. It is nice to know that my work is having a positive impact, and thanks for the feedback. To the best of our knowledge, according to quantum mechanics, it now appears that we do not live in a deterministic universe. I plan to soon have several more videos dealing with quantum mechanics, and I hope you will enjoy them too.
Hows it been going for you? Its been 7 years. I hope it's all gone very well.
@@allankaige7364 It's been good, I went on to get my bachelor's of science in computer engineering. At the time I was a high schooler that was going through a little existential crisis.
@@allankaige7364 +1, @belliumm, where has your curiosity taken you?
How’s it going now brdrrr
the song perfectly matched the topic=terrifying
extra:
if the result of the cross product is 0 (null vector), you have two parallel vectors
if the result of the dot product is 0, then you have two perpendicular vectors
God Bless you all.
Known as orthogonal vectors too :)
If both of em are zero then?
@@ashishkumarsharma1323 they both cannot be zero
Oh thanks...
@@Ghost____Rider of course they can, if one of the vector is zero
If you are wondering, the name of the song at the end is called William Tell Overture by Rossini. Please listen up the long one and not just the finale
3:53 when you finally realize you are One with the force.
The music was shocking, put some humorous light on this video. Loved it :P
She was serious
If you like this video, you can help more people find it in their UA-cam search engine by clicking the like button, and writing a comment. Thanks.
I like that this was voiced over by an anime voice actress.
Physics Videos by Eugene Khutoryansky use less
@@Higgs314 then what should i say?
BGM is so irritating
@@Higgs314 They have taught, dot product wrong, dont just believe all youtube videos
It's the best thing when I am searching for an animation and find my way back to this channel :) They make everything so much easier to visualize and understand
the ending music is so epic!
that moment when this 4 minutes video taught me about vector better than my 1 hour physic lecture....
Still dont get the idea behind the Dot and Cross product.. I'll just memorized the formula, then solve the problem, get an A+, never asked why, and go on with my life..
Every student ever .
and then forget it a year or two later*
Me, until it became important. Then I had to go back and actually learn it :/
all hail youtube for actually explaining shit
@@cinquine1 Same, I'm studying a degree in engineering and we're looking at the cross product between instantaneous angular velocity and perpendicular radius to find instantaneous linear velocity, and I have just realised are perpendicular to each other vectorially. So I guess I _do_ have to know about cross products after all! I was thinking to myself, "goddamit...."
Although..I've now found out it makes the whole process sooo much easier to understand calculating this all _vectorially_ using numerical unit vectors rather than taking a geometrical approach using their magnitudes instead (lots of confusing lines and trigonometry :/ )...which is why nowadays I'm actually starting to appreciate cross products a lot more than I had done in the past. That's something I never thought I'd say cause I found them hellish to understand in further maths. But they're actually fairing out to be _extremely_ useful when finding perpendicular magnitudes that are in a three dimensional space with each other...such is the case with angular motion. You just have to know about this fact beforehand. All you have to do is arrange two perpendicular vectors in a matrix with their unit vectors above, and find the determinant of this, for a third vector that's perpendicular to both. After that I was wondering why tf I never did this in the past cause it was so straightforward compared to how I was doing it with trig...
Saves time learning a bunch of different formulas when all you have to know is that (with unit vectors) : i = j *x* k ; j = k *x* i ; k = i *x* j ; and they are not commutative, so the reverse is the negative of those. Eureka moment for me XD (please tell me if I'm wrong about this :S )
You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link:
ua-cam.com/users/timedtext_video?v=h0NJK4mEIJU&ref=share
You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately.
Details about adding translations is available at
support.google.com/youtube/answer/6054623?hl=en
Thanks.
Please make video on constraint relation
i didn't expect such good use of music in a physics vid .....great job
shadow claw But this is basically maths.
This is math you moron
the most dramatic educational video on youtube.
Your other videos have been very explanatory. I like that they assume a novice viewer. Unfortunately I'm not following this one. It might help if you could detail some applications...like the time/speed/distance application in your calculus video, that made it clear how such a thing is used.
Loved the graphics along with blasted music to make sure viewer is attentive. Speaker voice gets the vote too!
Damn. I wanted to check my latest algorithmic ideas for sanity's sake, but stayed for the uncanninness.
Super helpful. Thank you!
I am glad my video is helpful. Thanks.
You here?!
WAIT TD BRICKS HERE?
Hahahahhaha I cracked up so hard when the dramatic instrumental music came when revealing the cross product direction. Never thought such an informative thing would do that. Now I'll definitely replay that moment in my head during the exam.
This is a fantastic video! No waffle. Not too slow, not too quick. Just perfect. Thank you for these amazing videos. They help me visualise what the hell is going on underneath all those ridiculous maths problems I solve haha 😅
Thanks for the compliments.
0:22 Wait, how could the 'length' of arrow representing the cross product be always equal to the 'area' of the parallelogram ?
it’s the numerical values are that equal
Thanks Clare.
Thank you, I was having a lot of difficulty in understanding the right hand rule, that demonstrated it perfectly!
I have been doing dot products for years now, no professors have ever explained it this well, and I think visually, so because no professors explained it, in my head I always said it was "how much the vectors are of each other." But this video helped me understand so much more.
Thanks for the compliment about my explanation. I am glad it was helpful.
This is the best illustration humanly possible!
+Fakher Halim, thanks for the compliment.
I'm a very visual person and could not understand why we use dot and cross product!!! this video literally saved me thank you !!!!!
Glad my video was helpful. Thanks.
that plot twist music at the end was perfect
Another beautiful visualization! These videos should be used in college as well as in universities!!
And, for totally unknown reasons, I would like to see a behind-the-scenes. Making videos like this must be a daunting task.
+Pär Johansson, thanks for the compliment. I would have to think about how to do a behind the scenes video. Thanks again.
This is the absolute best video I've ever seen that defines the dot product. All of the conceptual stuff that other videos try to explain pales in comparison to the simplicity of this visualization.
Thanks for the compliment about my video.
Music gave me flashbacks to the funeral of my great-grandfather, back in the Victorian era. Man those were some sad days.
this may be trivial to many, but to me, who only needs to remember crossproduct and dotproduct basics every 5 years or so, not doing vectors in that much detail usually using a blackbos, its easy to get your memories confused without such good visualization.
Don't stop you keep blowing my mind with simple stuff I have been using cross products for years and never realized it was just the area between the vectors
+tpespos, glad you found this interesting. More videos are on their way.
This was really helpful to visualize, but I'm still confused as to why multiplying 2 vectors results in a third one that forms a 90 degree angle from where the 2 vectors connect. Why does it happen?
This is what has been bugging me since i was introduced to vectors in school. This is my biggest lack of understanding in the fundamentals of physics. I have tried a lot but never found q clear explaination to this. So i have convinced myself that this rule is something that humans have agreed upon by conducting experimentation and finding results that just fit this type of calculation, and no one came up with it on thier own. While the dot product is very obvious and can be understood by doing your own thought experiments.
how length can exactly equal to area?
value of length is value of area
Equal in magnitudes I'm guessing is what they mean
Imagine a cardboard attached to the base of the vector. The length of the vector would, therefore represent the area. The length even represents force in Newton, and other things, so the units don't have much to do with it, it's about the magnitude.
The dot product visualization exploded my brain. I never knew it was this simple.
ok the question I always ask, what came first ? the cross and dot products or the physical phenomena that we needed to use these products for?
for example, the work = force * distance ... did we need to come up with the dot product to describe this phenomenon (that the work should be scalar, and it cares about the force component thats only towards the motion vector) , OR, we already have the dot and cross products and we used the dot here because it applies ??
I HOPE I GET AN ANSWER ....
Which editing software do you use?
sir you provide absolutely concept that others do not....it awesome....I loved it
Thanks.
so good thanks a lot...wished I knew about ur videos earlier. I wouldn't have faced any problem then...
Thanks. I am glad you like my videos.
This might be one of the most terrifying videos I have ever seen. When the music climaxes at the hand my heart dropped into my gut.
I just loved this video. I found the books to be too theoretical and never understood this concept until I watched this video. Definitely built my concept for lifetime. Thanks a lot 👏
I am glad my video was helpful. Thanks.
Underrated video with an OG climax
From the last 3 years I am studying about DOT and CROSS product but I today visualize it.. That's very nice and useful video... Thanks alot...
Thanks. I am glad my video was useful.
I started understanding the behavior of universe by the concept of your videos.. thanks.
can you please help me..? actually I want to make a model with the dot and cross product idea. please help me.
I come here every once in a while to watch the dramatic music
Wow I hadn't seen this link between particle handedness before now. Glad I found your channel
This is the best explanation on UA-cam!
Thanks for the compliment about my videos.
When i heard the title of video i remembered the video about electromagnetism and gyroscope i guess :)
Thanks eugene . Without you i would have stuck in physics very badly :)
+Shirshak Bajgain, glad to hear that my videos have been helpful. Thanks.
No one told me these logical expressions in school... Thank you.
You are welcome and thanks.
im not certain the arrow for the dot product was right. i couldnt figure out how you got the length of the red arrow.
from my understanding the dot product is one vector's projection onto another vector. i didnt quite see that. i gotta be missing something here.
This was.. memorable. Thank you!
that final hand move was epic!
Wonderful video recommended by my physics teacher pure gold
Killer visulaisation
I am glad you liked my video. Thanks.
@@EugeneKhutoryansky welcome Ma'am
I watched a bunch of videos on this subject and this was the first that made sense.
So cross product of two vectors = new vector and dot product of two vectors = a float number?
Your explanations are always very clear. Please continue making videos!
+Steven Karma, thanks for the compliment. More videos are on the way.
With the dot product, the component of the slanted vector must be multiplied by the length of the other original vector. The above video seems to indicate that the dot product is just the component of the slanted vector.
This was the most ominous way I've learned about the dot product and cross product
I hope I'm not the only person that cried watching this video.
aren't you a blessing.
Humbly grateful madame Eugene
Thanks.
I just searched for a demonstration
Thank God this video recommended for me
I am glad you liked my video.
Thank you so much... the language barrier and lack of proper explanation from my physics professor had my whole class confused
As a visual learner, thank you for this awesome visual explanation!
+roux ga roux, you are welcome, and thanks for the compliment about my explanation.
There are no visual learners. Periodt.
This is the good stuff. The right stuff.
The background music is William Tell Overture, and the video basically talks about ARROWS. I UNDERSTOOD THAT REFERENCE
Jeez that music on the RHR got me pumped to go into 16th-century battle
Superb 💖 touched my heart.thankyou so much.keep it up 💐
Thanks.
This 4 min clip is what i wanted when i was in school. Things would have been so easier to understand. Great that kids have access to this these days.
That intensifying music in the end really got me. LMAO.
I just found your channel today. I think I'm going to be a lifetime subscriber. :]
+Seth Connell, I am glad you found my channel, and I am happy to have you as a lifetime subscriber. Thanks.
What's the title and composer of the background music?
This was so superb....at the end of the video I felt dots connecting in my brain and at the very same moment the music was playing in the background!!!
Thank you so much!!! I've been struggling to visualize the dot product and cross product for the longesttt time. This animation helped me so much! As well as the circuit video I saw the other day!
Thanks. I am glad my videos are helpful.
You know, in high school I've always dreamed about how great it'd be if there were people knowledgeable about physics who could also animate complex topics they were discussing because there are some things that are hard to visualize. Can you imagine how cool a physics and animation major would be? :) There's also a lack of animated physics videos, but here you are animating physics videos very well and fulfilling one of my dreams! :D I'm very proud of you and the work that you do, and I'm forever grateful. I wish you the best in your endeavors. :)
EDIT: oh it's just a scalar. got confused from so much amazing visual animation :P
-isn't the dot product commutative? if it were then the resulting vector should be the same, but according to the animation it follows (is alligned with) only one of the original vectors (RED vector follows A not B). I understand the magnitude is the same, a.b.cosine, but the geometrical vector...? i'm confused-
exactly what I need in only 4 minutes. thanks
Thanks.
Excellent video, this is how it should be taught in physics classes
Thanks. I am glad you liked my video.
You videos were awesome like unfolding mathematics in to a movie , it makes looking outside world in terms of math . I thank you so much for your videos ,love from india
Thanks. I am glad you like my videos.
geez that ending... with the dramatic music, and the awkward hand... kinda scary ngl
What a music .... Really nice
saw the comment from you and 'It's Okay To Be Smart' on 'but did you die tho.' why are science UA-camrs so in love with that video?
great great great explanation thanks much
The best explanation i have ever seen!
Thanks for the compliment. I am glad you liked my explanation.
Thanks for using the captions
Really helped me
Because I'm not good at English
Superb presentation and explained in a simple manner.
Thanks for the compliment.
The music is William Tell Overture (Horse Race song)
Physics + Mathematics = One new subscriber.
+Sausage Biscuit, thanks. I am glad to have you as a subscriber.
No, thank you. :)
Man, nice music selection like Rossini's William Tell Overture with a beautiful animation for a math explanation. You got an inmediate new suscriber in myself!
Glad to have you as a subscriber. Thanks.
Thanks Eugene. This is a very good explanation.
+Sean Wiesen, thanks for the compliment.
absolute GOAT video :pray:
Mam you are a best teacher in the whole world
Thanks for the compliment.
when considering the second arrow (segment on dot product) the length of that side of the triangle is simply the x component of the the second arrow vector.
I love the classic background music
I have just couple of weeks away for tensor calculus exam and have found this video very helpful , i would request you to upload videos on cross tensor product of tensors and tensor product of tensors if possible
+saarvesh jayakumar, tensors are on my list of topics for future videos. Thanks.