Dot Product (1 of 2: Geometric interpretation)

[karunyaiyappan]

Beautiful explanation of the dot product - thank you so much for your visualization of the concept and overall passion for teaching!! I finally understand this.

[stevedoetsch]

We live in a time where the internet is full of videos anout mathematics to find at our discretion, and for some reason this is the one that best helped me understand the dot product of vectors. I am grateful for this video and the fact that I can search through the internet until I find the teacher that helps it make sense to me 😊

[hanss]

At 14:50, Eddie casually makes the quadratic formula make sense in about 10 seconds, and suddenly the thing becomes intuitive...

[skrdman]

I've been thinking of dot product as simply the product of one vector's magnitude with the component of another vector that is in the first vector's direction. Functionally, this is what the |a||b|cos(theta) expression does. I really like this thought process, because it shows why if we tried to use the dot product with 1 dimensional vectors, it would still work just like multiplication that we're used to. In 1 dimension, all vectors are parallel, so the cosine of the angle between them will always be 1 or -1.
Unfortunately, the same reasoning doesn't quite seem to apply to cross product, so maybe I'm wrong about the relationship between vector multiplication and scalar multiplication.

It did not occur to me to think of the cosine of theta as representing how much the two vectors are "working together", as if they were both force vectors. That's a nice way to think about it.

[kidusmulat]

Please do cross product I am begging you please

[Qaos]

Now I actually know what a dot product means, this is great

[MasterA]

Which app you are using for this tutorials, Is that Goodnote?

[Bazf]

That “independent” thing is kinda sketchy, some might confuse it with linear independence.

[BlueGiant]

I see nonstandard notation here that makes me wonder whether or not this is pedagogically wise. If these students arrived next year in a physics class using the Geometric Algebra notation developed by David Hestenes et al., would they pick up the new multivector notation quickly or feel confused by the polyglot? I've never seen tilde used to denote a vector before.
Why no mention of the projection definition of the dot product?

[ucLe-rtrz]

But what does Dot Product represent? And what problem does it solve?

[aslamsaja]

Hello, I ❤ your teaching by the way, do you have a phd in math?

[SimonFearn]

Great video but I still don't get why they are only scalers.

[johnnytoobad]

Are you with me Doctor Woo ?
Are you really just a shadow of the man that I once knew ?
Are you crazy..are you high ?
Or just an ordinary guy.
Have they really got to you ?
Are you with me Doctor ?

[MikhailFederov]

No offense but having the student speak adds zero value to the lesson

[WowUrFcknHxC]

I was always taught that the dot product a•b is the component of a in the direction of b. Basically, the magnitude of the vector projection of a onto b.