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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 )
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.
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.
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.
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
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 👏
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.
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 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!!!
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
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 :)
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. :)
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.
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!
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.
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
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.
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.
