"Imagine driving over a booster in mario kart at an angle and thinking about how much it boosts you." THANK YOU. That is a 1,000x more helpful than any other explanation I've seen. I now feel silly looking up an explanation for such a simple concept.
thank goodness, I've searched for days trying to find anyBODY to explain to me what the dot product is actually for and why it is used. They all just want to tell me how to use it. subbed!!!
This was absolutely brilliant. Cleared my confusions of what we get from a dot product. Very well explained. Thank you Better Explained, now I can go through any annoying physics question.
Oh man, you finally gave the intuitive idea I was looking for sooooo long. "Multiplying the same components" is what I needed. Now, I can finally understand that dot product is basically multiplication but we multiply the same components and since they usually don't have the complete same direction, we kind of project one to the other (kind of like shadowing one onto the other to get the true component which follows the same direction as the other) and then we happily multiply. Hopefully I didn't mess up writing this cuz I am bad at explaining my intuitions but thank you so much for this video!
mario kart boost panels do actually give you a boost in speed no matter in what direction you drive over it, so the analogy isn't exactly correct. However it would be correct for the conveyor belts on the map ""Toads Factory" in mario kart wii.
You rock! The similarity between the vectors. Great, that is what I was looking for, for days! Many thanks for creating this video. Very clear explanation!
wow. Sir you do not understand how useful this was to me. At such a remarkable timing as I just started calc 3 and physics 1 last week. Instant like and I am now subscribed.
Wow....the only explanation of this anywhere, at any time that gave me a sense of what the dot product truly means, after so many years! Thank you sir. I thought it was me, but now I realize that most teachers have no clue how to explain it. Don't stop making videos.
Sir i am from bangladesh. I have been looking for the REAL meaning of what dot product actually is from a long time. You really dont know HOW MUCH your video just help me. THANKS A LOT SIR. REALLY REALLY THANKS A LOT .
Right down to the heart of the matter. Thanks for getting to the point. Best explanation I have seen on the internet of this without fancy wow VFX. Subscribed.
Great explanation. I really like the visual approach where you broke down the vectors into horizontal/vertical and showed the distribution/overlap. That's super helpful for visualizing where the formula comes from.
It was i think the clearer explain of math principle i have ever seen, you really choose each words your will prononce, it was gold for me 💎. Thank you.
Thanks so much for your video here. I was looking everywhere for intuition on the dot product value and finally someone has explained it. Just subscribed
Ah, you were doing so well. Your "rotation method" is actually a projection method. If you rotated one vec onto another you'd just get the length. This is the cosine. Or maybe that's what you meant and I didn't get you. Perhaps you meant rotating the frame of reference to put one access on the x.
Thank you Khaled! I never thought about it as a rotation. Can you explain why the shorter vector is projected to the long one and not the other way around?
I wonder if mario kart is actually coded that way.. it always seemed to me like the direction did not affect the boost. Either way, this is still a great example for building intuition.
Still one question I have is why we multiply? I am not able to visualize why multiply A cos-theta . B? A cos-theta vector times of B? What is visual representation of multiplication? Kindly clarify.
I'll try to help you. let u and v be vectors. you know -u is just u flipped over, don't you? then -u · -v is exactly the same as u · v. (flipped over but we are just measuring the amount of u and v overlap as explained in the video). also, try to think the real numbers as 1-dimensional vectors. multiply them together. multidimensional vectors behave in a very similar way.
why in dot products only the same directional parts are being counted? why Ax.Ay = 0 ? Why mathematicians thought that this is a way of multiplication ? what has the intuition of multiplication been in their mind ? how they approach multiplication ?
I understand the Mario Kart one but for the solar panel one if you have the solar panel flat is the sun not hitting it at a 90-degree angle which means that you get the highest amount of energy? But if you do cos 90 you get 0 so that means no energy. Explain
I have a question; you mention two examples: the mario cart example and the solar panel example In the solar panel example, you say if the vectors are parallel; then no energy is absorbed and nothing is in common In the mario cart example, you say if the driver and the booster are parallel then maximum speed is gained because everything is in common These examples seem to cancel each other out; can you elaborate?
In the case of the solar panel, the vector representing the surface of the panel is perpendicular to the panel. When this vector is aligned with the vector representing the rays of the sun, the panel is perpendicular to the rays of the sun and the dot product is maximal. If you do a 90° rotation of the panel with it representative vector, you can observe that the vector is perpendicular to the rays of the sun (which means a dot product of zero,) and the panel is parallel to the rays of the sun (nothing passes through the panel).
It is the surface which absorbs the energy but not in the direction you have assumed. Think of the panel's surface as the surface of a water body. The light rays entering this medium are perpendicular to the surface but the absorption of these rays is in the same direction as of the rays. Thus the direction of absorption coincides (is parallel) to the light rays and these both directions are perpendicular to the surface. In a comparison, as the angle between the light rays and the surface tends to 0, the angle between the light rays and direction of absorption tends to 90 degrees. Therefore, this 90 degrees gives us 0 when dot product of light rays and direction of absorption is taken. Hopefully that should help. Although it has been 5 months, you might have figured this out already!
Better Explained ,it means let there r 2 vectors , a,b , then in the direction of b , influence of (a) vector would be zero ,. Then any object which is in the direction of (b) vector only feel influence of b's vector magnitude,. Is am right sir
"Imagine driving over a booster in mario kart at an angle and thinking about how much it boosts you."
THANK YOU. That is a 1,000x more helpful than any other explanation I've seen. I now feel silly looking up an explanation for such a simple concept.
SAME. I've been re-reading a textbook chapter on Dot product, not finding a way to make it visually relevant, but this example helped a lot.
Lol I would say this is the best explanation possible
thank goodness, I've searched for days trying to find anyBODY to explain to me what the dot product is actually for and why it is used. They all just want to tell me how to use it. subbed!!!
couldnt have said it any better
Exactly! , I don’t understand why mathematics teachers don’t teach like this.
That Mario kart boost analogy is gold! Thank you for posting this video
This was absolutely brilliant. Cleared my confusions of what we get from a dot product. Very well explained. Thank you Better Explained, now I can go through any annoying physics question.
Best Dot Product discussion I have seen!
Oh man, you finally gave the intuitive idea I was looking for sooooo long.
"Multiplying the same components" is what I needed.
Now, I can finally understand that dot product is basically multiplication but we multiply the same components and since they usually don't have the complete same direction, we kind of project one to the other (kind of like shadowing one onto the other to get the true component which follows the same direction as the other) and then we happily multiply.
Hopefully I didn't mess up writing this cuz I am bad at explaining my intuitions but thank you so much for this video!
His explanation makes all other videos look unreasonably complicated, remarkable job, sir. Thank you.
mario kart boost panels do actually give you a boost in speed no matter in what direction you drive over it, so the analogy isn't exactly correct. However it would be correct for the conveyor belts on the map ""Toads Factory" in mario kart wii.
You rock! The similarity between the vectors. Great, that is what I was looking for, for days! Many thanks for creating this video. Very clear explanation!
bruh i spent the whiole day trying to understand, then i watched this... thank you you beautiful American man
That Mario Cart analogy... My god, all math textbooks need to be revamped with these sorts of references.
wow. Sir you do not understand how useful this was to me. At such a remarkable timing as I just started calc 3 and physics 1 last week. Instant like and I am now subscribed.
Wow....the only explanation of this anywhere, at any time that gave me a sense of what the dot product truly means, after so many years! Thank you sir. I thought it was me, but now I realize that most teachers have no clue how to explain it. Don't stop making videos.
Bruh that mario kart example was genius, thank you
Sir i am from bangladesh. I have been looking for the REAL meaning of what dot product actually is from a long time. You really dont know HOW MUCH your video just help me. THANKS A LOT SIR. REALLY REALLY THANKS A LOT .
Right down to the heart of the matter. Thanks for getting to the point. Best explanation I have seen on the internet of this without fancy wow VFX.
Subscribed.
Great explanation. I really like the visual approach where you broke down the vectors into horizontal/vertical and showed the distribution/overlap. That's super helpful for visualizing where the formula comes from.
I don't think i have ever been more mind blown in my life. thank you
Honestly, I can't remember/learn anything until the context of it is clear, and this helped SO much 🙏👍
Thank you! The solar panel and mario kart examples gave me an actual use case and reason why we use the dot product. Well done!
Fantastic explanation! Please keep up the good work. The world needs more great math teachers.
It was i think the clearer explain of math principle i have ever seen, you really choose each words your will prononce, it was gold for me 💎. Thank you.
I understood it. Perfect explanation. I am now using it to calculate the distance of a point and a segmented line. Really, thank you!
Why are we multiplying the components ?
dude, you are a legend, your didactic is so good
You rock man ! now I understand where the algebraic definition comes from
Best explaination I've come across so far! :) On to cross products...
Finally understood what the dot product actually does and where its applied,indeed better explained thanks for this video
I like the name of your channel. That's how it should be!
I can't describe how helpful this was! THANK YOU!!
happy math ? thats like the most romantic thing anyone ever said or will say
Thanks so much for your video here. I was looking everywhere for intuition on the dot product value and finally someone has explained it. Just subscribed
Ah, you were doing so well. Your "rotation method" is actually a projection method. If you rotated one vec onto another you'd just get the length. This is the cosine. Or maybe that's what you meant and I didn't get you. Perhaps you meant rotating the frame of reference to put one access on the x.
This is the greatest explanation ever! Thank you so much.
GREAT explanation. Thank you! And I hope you'll continue to upload videos (:
Thank you!
the sleekness screams professional but the glasses scream true professional
👍
This is truly great! Thank you very much. I hope you have a lot of inspiration in your life because you do wonderful things.
OMG YOU TAUGHT THIS TEN TIMES BETTER THAN MY MATH TEACHER> THANK YOU
Excellent video and good slides
Man you saved my life :). Thanks for this great work
This gives me the best intuition! thank you
Thank you Khaled! I never thought about it as a rotation. Can you explain why the shorter vector is projected to the long one and not the other way around?
Chela Weitzel thank you!
I wonder if mario kart is actually coded that way.. it always seemed to me like the direction did not affect the boost.
Either way, this is still a great example for building intuition.
Still one question I have is why we multiply? I am not able to visualize why multiply A cos-theta . B? A cos-theta vector times of B? What is visual representation of multiplication? Kindly clarify.
Please include cases where the directions are opposite. Thank you. Great video
I'll try to help you. let u and v be vectors. you know -u is just u flipped over, don't you? then -u · -v is exactly the same as u · v. (flipped over but we are just measuring the amount of u and v overlap as explained in the video).
also, try to think the real numbers as 1-dimensional vectors. multiply them together. multidimensional vectors behave in a very similar way.
Whoever you are: Thanks!
this is mind blowing information imo
why in dot products only the same directional parts are being counted? why Ax.Ay = 0 ? Why mathematicians thought that this is a way of multiplication ? what has the intuition of multiplication been in their mind ? how they approach multiplication ?
Where can we find the text pages you have displayed? Is that from a book or online coirse?
This is what genious looks like
I understand the Mario Kart one but for the solar panel one if you have the solar panel flat is the sun not hitting it at a 90-degree angle which means that you get the highest amount of energy? But if you do cos 90 you get 0 so that means no energy. Explain
brilliant explanation.
Great explanation
Thanks a lot, I needed to know more on dot product projection/similarity relationship between vectors, got my answer.
Shit, I'm in luck; no fucking whack accent! Gold!
But does this give us a scalar product and not a vector product
This was just perfect. Thank you so much!!
I have a question; you mention two examples: the mario cart example and the solar panel example
In the solar panel example, you say if the vectors are parallel; then no energy is absorbed and nothing is in common
In the mario cart example, you say if the driver and the booster are parallel then maximum speed is gained because everything is in common
These examples seem to cancel each other out; can you elaborate?
In the case of the solar panel, the vector representing the surface of the panel is perpendicular to the panel. When this vector is aligned with the vector representing the rays of the sun, the panel is perpendicular to the rays of the sun and the dot product is maximal. If you do a 90° rotation of the panel with it representative vector, you can observe that the vector is perpendicular to the rays of the sun (which means a dot product of zero,) and the panel is parallel to the rays of the sun (nothing passes through the panel).
It is the surface which absorbs the energy but not in the direction you have assumed.
Think of the panel's surface as the surface of a water body. The light rays entering this medium are perpendicular to the surface but the absorption of these rays is in the same direction as of the rays.
Thus the direction of absorption coincides (is parallel) to the light rays and these both directions are perpendicular to the surface.
In a comparison, as the angle between the light rays and the surface tends to 0, the angle between the light rays and direction of absorption tends to 90 degrees.
Therefore, this 90 degrees gives us 0 when dot product of light rays and direction of absorption is taken.
Hopefully that should help. Although it has been 5 months, you might have figured this out already!
This is a really great explanation, thanks!
exactly what I need, great video, subscribing.
Great video, very well explained. Thank you!
Super helpful. Thank you
Bhai maje aage
What is that picture behind you?
amazing you are!!! THANK YOU.
bruh ty sm this helped my mcat prep
What a babe
Wow. Thank you so much!
Where did you go my neurodivergent brain needs you to explain more maths 😊
how does this extend to the dot product of 2 matrices?
Thanks, it was a clear expression.
Make more videos please!
great video!
I understand it now, but I think some animated vectors would have helped explain it.
amazing
Best! BEST!! BEST!!!
Best!
you are amazing
Ty!!!
extremely well explained and kept simple, amazing
This is great.
You're a blessing! Thank you so much, it wasn't making any sense
Why dot product of 90° is zero why
If you travel 1km North, how far East have you gone?
Better Explained zero ,. I got it sir ,, many thnks
Better Explained ,it means let there r 2 vectors , a,b , then in the direction of b , influence of (a) vector would be zero ,. Then any object which is in the direction of (b) vector only feel influence of b's vector magnitude,.
Is am right sir
Ily.
If I don't play Mario, this video decrease 40% to makes me understand
ok , but i have still questions
no such thing as better explx or not, me explx/can explx anyx by anyx no matter what and anyx can be perfect
?????
u might be feel dumb untill find this video
help
Isn't this pretty?