Cross Product and Dot Product: Visual explanation

Visual interpretation of the cross product and the dot product of two vectors.
My Patreon page: / eugenek

[@EugeneKhutoryansky]

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.

[@ikrishna06]

I like your explanation 😉😁

[@jollyriju2919]

I can't find gear symbols under this video

[@NicksDomain101]

I love the terrifying climax of the music when they show the hand

[@ToLearnDev]

it makes me scared of math

[@Floppylikescheese]

It's like they showed the ultimate universal secret. It's in the HAND!

[@MatomeQuestMoremi]

NicksDomain101 Yup. Excellent but awkward.

[@Bemmu]

Thanks, I spilled my drink laughing at your comment.

[@user-bv6bi2sz8r]

This music makes me feel like I am some Mathematicians thinking hard of a very tricky problem in 18th century.

[@rmsvideos1335]

Came for cross product, left with existential crisis.

[@pipturbine473]

Hahaha legend

[@thanhvinhnguyento7069]

RMSVideos oh god

[@arpitjohri9743]

Same bro, same

[@robinranabhat3125]

legend

[@vivekstreme1994]

Lol

[@SirBagelFace]

This video has such an ominous energy and I was not prepared for it.

[@ProGaming-kb9io]

The music is like: Harry Potter and the Vectors calculations chamber.

[@RedFox-dj7di]

XD

[@anu_1702]

ROTFL

[@edgbaston149]

True

[@ishworshrestha3559]

Ok

[@danieljoseph2647]

the ending song was perfect

[@marco_robert]

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...

[@EugeneKhutoryansky]

Thanks for the compliments.

[@danielstewart3507]

Marco, 4) Amount of effort. Not mound of effort.

[@marco_robert]

@@danielstewart3507 Yeah 😅

[@belliumm]

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.

[@EugeneKhutoryansky]

+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]

Hows it been going for you? Its been 7 years. I hope it's all gone very well.

[@belliumm]

@@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.

[@MDMAx]

@@allankaige7364 +1, @belliumm, where has your curiosity taken you?

[@peeyush8]

How’s it going now brdrrr

[@ccd7339]

the song perfectly matched the topic=terrifying

[@elijahizere]

The music was shocking, put some humorous light on this video. Loved it :P

[@mgtowindia9549]

She was serious

[@wurttmapper2200]

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

[@LuRybz]

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.

[@TheIsrraaa]

Known as orthogonal vectors too :)

[@ashishkumarsharma1323]

If both of em are zero then?

[@Ghost____Rider]

@@ashishkumarsharma1323 they both cannot be zero

[@rishitasf]

Oh thanks...

[@johnrubensaragi4125]

@@Ghost____Rider of course they can, if one of the vector is zero

[@sy_ox]

3:53 when you finally realize you are One with the force.

[@EugeneKhutoryansky]

If you like this video, you can help more people find it in their KZbin search engine by clicking the like button, and writing a comment. Thanks.

[@matthewburson2908]

I like that this was voiced over by an anime voice actress.

[@Derick_286]

Physics Videos by Eugene Khutoryansky use less

[@Derick_286]

@@Higgs314 then what should i say?

[@meenumeeny99]

BGM is so irritating

[@sushilghildiyal9319]

@@Higgs314 They have taught, dot product wrong, dont just believe all youtube videos

[@kevinz11ca]

the ending music is so epic!

[@EugeneKhutoryansky]

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: kzbin.info_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.

[@akshatmandloi3278]

Please make video on constraint relation

[@cphVlwYa]

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

[@abhishekbhattacharjee4639]

i didn't expect such good use of music in a physics vid .....great job

[@heliosaeon1458]

shadow claw But this is basically maths.

[@Artaxerxes.]

This is math you moron

[@1mursyid1]

that moment when this 4 minutes video taught me about vector better than my 1 hour physic lecture....

[@fazaldudha5728]

Loved the graphics along with blasted music to make sure viewer is attentive. Speaker voice gets the vote too!

[@imme_fr]

the most dramatic educational video on youtube.

[@mikkolodeon7053]

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..

[@uathrhsalim]

Every student ever .

[@OneDerscoreOneder]

and then forget it a year or two later*

[@cinquine1]

Me, until it became important. Then I had to go back and actually learn it :/

[@ericklestrange6255]

all hail youtube for actually explaining shit

[@Dragoneer]

@@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 )

[@TDBRICKS]

Super helpful. Thank you!

[@EugeneKhutoryansky]

I am glad my video is helpful. Thanks.

[@sharonjoe7535]

You here?!

[@HyperDevv]

WAIT TD BRICKS HERE?

[@missakissa987]

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.

[@Test-ri2kr]

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 😅

[@EugeneKhutoryansky]

Thanks for the compliments.

[@zEre326]

I'm a very visual person and could not understand why we use dot and cross product!!! this video literally saved me thank you !!!!!

[@EugeneKhutoryansky]

Glad my video was helpful. Thanks.

[@SteichenFamily]

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.

[@flamestorm06]

Thank you, I was having a lot of difficulty in understanding the right hand rule, that demonstrated it perfectly!

[@fakherhalim]

This is the best illustration humanly possible!

[@EugeneKhutoryansky]

+Fakher Halim, thanks for the compliment.

[@shipwreck9146]

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.

[@EugeneKhutoryansky]

Thanks for the compliment about my explanation. I am glad it was helpful.

[@_AnmolGupta]

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...

[@EugeneKhutoryansky]

Thanks. I am glad my video was useful.

[@samirkhosrowshahi7928]

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.

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@tpespos]

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

[@EugeneKhutoryansky]

+tpespos, glad you found this interesting. More videos are on their way.

[@MAG_104]

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.

[@b43_pranjalvyas76]

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!!!

[@jhoan7189]

perfect illustration of complex vector subjects. thank you!

[@ashutoshpatel5030]

sir you provide absolutely concept that others do not....it awesome....I loved it

[@EugeneKhutoryansky]

Thanks.

[@KushG420]

aren't you a blessing. Humbly grateful madame Eugene

[@EugeneKhutoryansky]

Thanks.

[@flare909]

I've been waiting for this video forever!!!!!! Thank you!!!!

[@EugeneKhutoryansky]

+flare909, the wait is finally over. Glad you liked it.

[@jocomo5054]

I just searched for a demonstration Thank God this video recommended for me

[@EugeneKhutoryansky]

I am glad you liked my video.

[@angeldavidstarrmauas8322]

Amazing! Finally I get to understand this! The single best explanation I could even fathom! Just awesome! Thanks so much!

[@EugeneKhutoryansky]

Glad my explanation was helpful. Thanks for the compliments.

[@MathFortress]

More on the cross product: kzbin.info/www/bejne/oKGulKOpg6yafNE

[@cloudyclo]

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!

[@EugeneKhutoryansky]

Thanks. I am glad my videos are helpful.

[@cloudyclo]

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. :)

[@StevenKarma]

Your explanations are always very clear. Please continue making videos!

[@EugeneKhutoryansky]

+Steven Karma, thanks for the compliment. More videos are on the way.

[@etherealbae2160]

This was.. memorable. Thank you!

[@lightoftheFather_]

This is the best explanation on KZbin!

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@Feynstein100]

Great explanation, Eugene. Can't wait for your next video.

[@EugeneKhutoryansky]

+Feynstein100, thanks. Glad you liked it. I am working on my next video, which will be on Quantum Wave function visualization.

[@TheRabidCabbage]

I watched a bunch of videos on this subject and this was the first that made sense.

[@amritpatra6857]

Wonderful video recommended by my physics teacher pure gold

[@amritpatra6857]

Killer visulaisation

[@EugeneKhutoryansky]

I am glad you liked my video. Thanks.

[@amritpatra6857]

@@EugeneKhutoryansky welcome Ma'am

[@chhavigupta2802]

so good thanks a lot...wished I knew about ur videos earlier. I wouldn't have faced any problem then...

[@EugeneKhutoryansky]

Thanks. I am glad you like my videos.

[@IamArob0t]

that plot twist music at the end was perfect

[@basitsultan2854]

Superb 💖 touched my heart.thankyou so much.keep it up 💐

[@EugeneKhutoryansky]

Thanks.

[@shafiqreshid4288]

Underrated video with an OG climax

[@parjohansson3118]

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.

[@EugeneKhutoryansky]

+Pär Johansson, thanks for the compliment. I would have to think about how to do a behind the scenes video. Thanks again.

[@bloggervista]

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 :)

[@EugeneKhutoryansky]

+Shirshak Bajgain, glad to hear that my videos have been helpful. Thanks.

[@smitititecnosoft]

I started understanding the behavior of universe by the concept of your videos.. thanks.

[@BrunoSdeLima]

Fantastic. These tools are priceless for students!

[@AlmightyXI]

Wow I hadn't seen this link between particle handedness before now. Glad I found your channel

[@Leo-sh1ih]

As a visual learner, thank you for this awesome visual explanation!

[@EugeneKhutoryansky]

+roux ga roux, you are welcome, and thanks for the compliment about my explanation.

[@dariocardajoli6831]

There are no visual learners. Periodt.

[@ollllj]

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.

[@MunchyMallow]

The dot product visualization exploded my brain. I never knew it was this simple.

[@Pri-tf9iv]

this video was soo needed!! thank you sooo much!

[@EugeneKhutoryansky]

+Arpita Singh, you are welcome, and thanks.

[@sukanya3411]

Music gave me flashbacks to the funeral of my great-grandfather, back in the Victorian era. Man those were some sad days.

[@leyre9989]

Thanks so muuuuuch!! I already understood the dot product but i couldn't visualise the cross product so this has been soo useful :)

[@EugeneKhutoryansky]

Thanks. Glad to hear that my video was useful.

[@ryanw.4983]

This really helped my understand this concept! Thank you!

[@EugeneKhutoryansky]

Glad my video was helpful. Thanks.

[@nandikakaul6979]

Wow. This was so helpful! Thank you

[@Muuip]

Great visualization! Much appreciated!

[@EugeneKhutoryansky]

Thanks.

[@sethconnell3497]

I just found your channel today. I think I'm going to be a lifetime subscriber. :]

[@EugeneKhutoryansky]

+Seth Connell, I am glad you found my channel, and I am happy to have you as a lifetime subscriber. Thanks.

[@busraa_]

No one told me these logical expressions in school... Thank you.

[@EugeneKhutoryansky]

You are welcome and thanks.

[@intuitivepariacademy]

can you please help me..? actually I want to make a model with the dot and cross product idea. please help me.

[@savemey2jnavi]

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!

[@EugeneKhutoryansky]

Glad to have you as a subscriber. Thanks.

[@jiaqihuang7762]

Thank you for this video! That makes so much sense!

[@EugeneKhutoryansky]

I am glad you liked my video.

[@samrat6720]

This was the most ominous way I've learned about the dot product and cross product

[@dougvitagliano7512]

These videos are awesome! Thanks

[@EugeneKhutoryansky]

+Doug Vitagliano, I am glad you like them.

[@abhishekcherath2323]

Great work. Thank You.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@1schwererziehbar1]

This is the good stuff. The right stuff.

[@kingkirby8960]

Physics + Mathematics = One new subscriber.

[@EugeneKhutoryansky]

+Sausage Biscuit, thanks. I am glad to have you as a subscriber.

[@kingkirby8960]

No, thank you. :)

[@tuandunglai2491]

how length can exactly equal to area?

[@technus102]

value of length is value of area

[@Dragoneer]

Equal in magnitudes I'm guessing is what they mean

[@lightoftheFather_]

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.

[@poisenbery]

these videos are amazing

[@EugeneKhutoryansky]

Thanks for the compliment.

[@itz.zaid__4410]

Mam you are a best teacher in the whole world

[@EugeneKhutoryansky]

Thanks for the compliment.

[@rgokulram9925]

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

[@EugeneKhutoryansky]

Thanks. I am glad you like my videos.

[@jvillalobos6988]

that final hand move was epic!

[@ilijamajcen5426]

exactly what I need in only 4 minutes. thanks

[@EugeneKhutoryansky]

Thanks.

[@sarikanigar5936]

0:22 Wait, how could the 'length' of arrow representing the cross product be always equal to the 'area' of the parallelogram ?

[@clarelee3397]

it’s the numerical values are that equal

[@azysgaming8410]

Thanks Clare.

[@thestarinthesky_]

The best explanation i have ever seen!

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad you liked my explanation.

[@seanwiesen7418]

Thanks Eugene. This is a very good explanation.

[@EugeneKhutoryansky]

+Sean Wiesen, thanks for the compliment.

[@EigenA]

Jeez that music on the RHR got me pumped to go into 16th-century battle

[@madch3mist]

Nice animation and succinct differentiation between the scalar and cross products.

[@joeye6556]

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?

[@AMANSINGH-tb6pj]

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.

[@desrepeerc206]

Excellent video, this is how it should be taught in physics classes

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@demartlectus1181]

The music is William Tell Overture (Horse Race song)

[@balajid1157]

Superb presentation and explained in a simple manner.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@conceptscracked8281]

Explained Well, teacher! However, let me summarize the video for further clarification. CROSS PRODUCT 1) The MAGNITUDE of the vector resulted in cross product is the AREA OF PARALLELOGRAM formed by the two vectors. 2) The DIRECTION of the vector resulted in cross product is always PERPENDICULAR to the original vectors. 3) A*B = -B*A (Reversing the order of the original vectors changes only the direction of the final vector) DOT PRODUCT 1) The MAGNITUDE of the vector resulted in dot product is the PRODUCT of the length of first vector multiplied by the length of PROJECTION of second vector on the first vector. 2) No vector is resulted in dot product; it is always a scalar number. 3) A.B = B.A (Reversing the order of the original vectors do not change the final scalar value)

[@The_MatEngineer]

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.

[@akashm9052]

amazing video , amazing work 👌 keep it up👍

[@EugeneKhutoryansky]

Thanks.

[@Anna-qp1fi]

Excellent explanation, thank you!

[@EugeneKhutoryansky]

Thanks. I am glad you liked my explanation.

[@elaine3867]

Thank you so much. It really helped my understanding on the topic

[@EugeneKhutoryansky]

I am glad my video was helpful. Thanks.

[@hairyfiddler2274]

That helped a lot thanks 🙏🏼

[@fightforfitness2256]

Thanks for your effort .

[@UnfilteredCactus]

Thank you so much... the language barrier and lack of proper explanation from my physics professor had my whole class confused