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Pot product basically tell how two (or many) things close each other. that's the logic behind AI machine learning. In AI, everything is represented by vector(s). using dot product operation , we can automatically( use GPU) to calculate how two thing related each. we find Paris vector dot to France vector , the result value is almost 1. while Beijing vector dot France vector is almost zero, so machine (AI) "learn" , Paris is more close France than China.

Not gonna lie writing components as x_a is crazy...

I remember when I did this last year as a cyber I was so happy to see that cube question, it was one of the only ones I could do

11:33 you didn't multiply -6.3g x 2 which leads to the tension being wrong. Actual tension is 31.18 N

Yh the car analogy rlly helped when i heard of it i think it was from eddie woo who told it to me

Thank you so much...! 😊

Long story short, imaginary number just spins the x-axis in 90 degress. Essentially it's a prototype y-axis in the 1D plain. Let say x= 3+ 2i if you wanna plot it in the graph then it would be x = 3, y = 2. Man I wish they told us stuff like this in school so I can ace my math exams 😭.

What is the whiteboard?

This is a great video. It's the content like this that we miss in our schools & universities. Pretty basic but profound. Thanks a lot for this!!! great video. Can you recommend any decent content, write up or a video to understand Eigen values and Eigen vectors. ?? We'll be grateful if you can make one.

Banger

Actually they should have made the Real Number axis, the y-axis : and the Imaginary Number axis, the x-axis. That means that "e to the power "i" theta" would go clockwise as theta increases. It does incalculable damage to the psyche to live in a society where things just whiz around any old way. We need to whiz around in a clockwise direction.

heyy! liked the explanation, very intuitive!

WAITING FOR PART 2!!!

What platform do you use to draw?

Have you thought about making a video explaining Euler's identity?

Why is it better this way? I feel like you're doing the same just with more steps

I love your gangster approach to mathematics. I will keep watching. A job well done sir!

Great video man, keep up the good work

Nicely done. I think it is better than the way I do. here is how I do it. if α is the angle between x-axis and vector b, and θ is the angle between vector a and vector b. you can write xb = bcosα and xa = acos(α+θ) yb = bsinα and ya = acos(α+θ) now if you eliminate α, you end up with something like xa = (a/b)xb cosθ - (a/b)yb sinθ and ya = (a/b)xb sinθ + (a/b)yb cosθ Now if you eliminate sinθ from the above equations, you'll magically see the result turning into xaxb + yayb = (a/b)(xb^2 + yb^2)cosθ but (xb^2 + yb^2) is just b^2. so, xaxb + yayb = (a/b)b^2 cosθ xaxb + yayb = ab cosθ which is what we want!

Loving these videos, you've earned yourself a subscriber. Looking forward to more of these intuitive type vids!

I love the analogy and no background music that too straight tot the point. Immediately subbed

I liked the explanation at the start of component forces but, the dot product using this car analogy leads to a couple issues I feel. The dot product outputs 50 (N...) for the first two scenarios, for the "overall force we are pushing on the car" but, this is physically speaking incorrect for the car, the result is 15N newton in the positive x direction, In this scenario the dot product moreso would find how similar(+) or different(-) the two forces are (like when you say how much your friend is helping you) BUT while using an abstract SCALAR metric, like how you knew to remove the N sign from your different dot product examples. It doesn't work in Newtons, but if you did want to then you would: 1. compare the forces in Newtons, by subtracting each force's x & y component from the other's to see the difference 2. find the "overall force we are pushing on the car" in Newtons, by adding each force's x & y component together and use Pythagoras to summarise the information into an amount of Newtons and resulting direction I'm sure this isn't news to you considering you have a maths RUclips channel, but in this example it just happens that physics denies that the result is how the dot product processes two forces... Mechanical work is an example that is more fitting in physics for the dot product! Good interesting video Irish brother

Correction: at 2:23, I should’ve written |a|^2 (the magnitude of vector a squared), but I forgot to write the exponent. Sorry about that!

Hi again. Think the answers for Q1(c) might be incorrect? I'm getting 2.59s and 5.41s and someone else verified them also.

Love to see this still going

Thanks a million for the videos.....just using them to check my own here. Just wondering would the radius of the horizontal circle in parts (ii) and (iv) not be 10SinB as opposed to 10? My solution matches yours in every other way outside of that, so I'm getting different answers for v and the coefficient of friction.

nicest question on the paper sadly

Big day tomorrow lads. Thanks a million for this one.

Hi, do you have an email address I can use to send you a message? Thank you!

Привет, я как русский слушатель, знающий английский ничего не поняла 😂, но ничего страшного, главное продолжайте снимать дальше! Я уверена, что это очень полезно!

Best video out there for this. Thankyou. 😇Very helpful.

Amazing! thanks for the video Edit: LC Exam in 2 days, Ill get a h1 on this q only because Of JT maths. Thanks JT

howd u get the angle and initial velocity on the moon if the time wuda been different?

2:52 the bruh made me laugh so loud 💀

Thanks for taking the time to do all these videos, much appreciated.

Hello, Great video ,very helpful for my project. I'm just wondering if, when u added the first image of the equation with u =ucos(angle) if u meant to drop the t in the power? and if so why?

*Errors* At 2:29 - I think the characteristic length can be taken to be the diameter of the ball (0.04m). At 5:06 - I accidentally set Re=8*10^3 instead of 8*10^4. The same answer is still obtained (Cd = 0.25), but I just wanted to point that out. Most websites said that Cd = 0.25 anyway, so I think using that value is okay. Please leave a comment if you find any others!

Good work

Ayoooo