Vector dot product and vector length | Vectors and spaces | Linear Algebra | Khan Academy
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- Опубликовано: 15 апр 2025
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Definitions of the vector dot product and vector length
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hi Khan sir, Loved your videos, they are helping me to learn machine learning.
"Hopefully you are taking this BEFORE college..." *looks around* so is it bad that I'm gonna graduate next semester and I'm just now taking this class? :O
I don't know anyone who took linear in high school, I think it's pretty normal to take it somewhere halfway to the end of your undergraduate studies. I just learned the basic of vectors in high school physics
#Taking it first year of high school
well, I'm looking this to learn machine learning...
Most public high schools don't even offer linear algebra, so don't feel bad. Hey all we had was calculus and pre-calculus. This was just offered to me mid uni.
same :D
You don't seem to annotate your videos with links but ~7:38 would be an excellent place to link to a video on metrics if you have made one (I haven't checked, but I bet it's there)
What about the Hadamard product? I don't understand why that's not taught first when it comes to vector mul.
best prof ever hands down
I was initially confused because I was watching this video to help write a custom function to find the dot product but Unity defines the dot product as "the magnitudes of the two vectors multiplied together and then multiplied by the cosine of the angle between them." I learned that there are two methods to find a dot product, although this video only mentions one of them, while Unity uses the other. Both methods yield the same result.
Yes, there are two ways of doing it. One (the way Sal showed) is more convenient if you are working with linear components (rectangular coordinates) the other (the Unity definition) is more convenient for working with vectors described as a length and an angle (polar coordinate).
I'm interested in representing a known length and direction (in 3 dimensions) as a unique vector. I'll keep watching.
as good as ever, thank you khan academy
Thank you so much!! You are part of the reason I passed my first semester in year 10 :D
how are things going for u now?
I always learn physics only in khan academy. It is great.
THANK YOU SOOOO MUCH!!!
The first thing that came into my mind when he showed the Dot Product was " What in the world is it used for"? But I'm only half way thru the video.✨
Thank you so much!
finally i get it! thanks so much.
Is it compulsory that the the multi-dimensions other than 3d space would be perpendicular to each other ?
then... what about: a*b=||a||*||b||cos(theta)?
That's right. Both sides will lead to the same answer. Just try it with any numbers for intuition. It can also be proved.
@@y.z.6517 wait i tried this, and they were different
@sahayester that's a program coming with an external hardware called drawing pad. So he draws it on the pad and pad sends drawings to pc instantly =)
Thank you
reminds me of discrete maths I did in my first year software engineering degree. lol good old days.
I have to raise an eyebrow at some of your comments regarding multidimensional spaces, especially the one about length somehow changing after 3 dimensions. Anyone with an understanding of how length works in 2 and 3 dimensions knows how it works in n dimensions, it's all the same.
Thanks!
4:54 lmao nope taking it at a college level degree 😂
am I the only one confused why matrix multiplication comes before dot products in the playlist? or is that the normal order that you learn this
thank god for these videos btw
If scalar is not a vector, then why does the multiplication of a scalar with a vector affects the direction of vector. For example scalar -5 multiplied with a vector scales magnitude by 5 but also reverses the direction.
It just scales in the opposite way, when you look at it from a perspective of a linear combination it's just a line, and every dot on there can be represented by multiplying the vector with some scalar
who can explain, what is then |a|? by this ||a|| we taking length of vector, i understood, but what then we take by this |a|? It has the same meaning, isn't it? I little bit confused. Please someone explain
JOFFREY BARATHEO
It basically means that you're taking the SCALAR form of vector a, neglecting its direction.
Which is the formula that puts uses the magnitudes?
Thought when he said "let me do some examples, because this might seem abstract"
That he would do concrete, real -life application. Instead, he just multiplied two numbers.
Abstraction remains.
What software is that
True!
nice
Did u represent the vector as column vector in matrix form? Im confused how u took product (dot) of 2x1 by 2x1 matrix, as no. of columns of 1st matrix is not equal to number of rows in second?
look , I've been thinking of matrix multiplication, dot product, cross product ect. these are all human convention , and you'll find them useful in some applications later on , I advise you don't think about these human conventions too often because they indeed don't have a proof ! but you gonna know that they will simplify a lot of things and they have a lot of applications , just watch these videos one after the other , after going through the course you will get some intuition and you'll know how these concepts are related .. In linear algebra , people often represent vectors as columns .. dot product is not like matrix multiplication this gives you a scalar "value" and that gives you another matrix .. you gonna see the relationship between concepts later on , you just have to keep watching these videos , I was like you confused but after a while I realized what's going on
length of vector is magnitude of vector. correct ?
Does anyone know why cosine doesn’t come into play in these examples?
Wondering the same thing
trippy
Ya, I also realized that, 5 minutes later.
Vector dot, doctor vet
You really didn't think it would be useful to explain what a dot product actually represents and why you might use it?!
In my trigonometry book, it literally says the "dot product of two vectors results in a scalar rather than a vector". There really is no explanation as to what it actually represents besides being a number. I think it was developed before anyone really had any use for it, and now the dot product is used to find the angle between two vectors and for finding projections of one vector on to another.
সালাম বস !!!
hi shs
Just MS paint I think lol
How is this useful?
nah