Vector dot product and vector length | Vectors and spaces | Linear Algebra | Khan Academy

Definitions of the vector dot product and vector length

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

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[ZachWhosoever]

"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

[indiansoftwareengineer]

hi Khan sir, Loved your videos, they are helping me to learn machine learning.

[ThePigscanfly]

Thank you so much!! You are part of the reason I passed my first semester in year 10 :D

[stfran]

I'm interested in representing a known length and direction (in 3 dimensions) as a unique vector. I'll keep watching.

[justinli]

as good as ever, thank you khan academy

[tomysshadow]

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.

[sdfsgdsfgsdfg]

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)

[kamrannasir]

Is it compulsory that the the multi-dimensions other than 3d space would be perpendicular to each other ?

[fiskefyren]

then... what about: a*b=||a||*||b||cos(theta)?

[jembergebeye]

I always learn physics only in khan academy. It is great.

[Nwgo]

@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 =)

[moonhowler]

What about the Hadamard product? I don't understand why that's not taught first when it comes to vector mul.

[bakhtn]

reminds me of discrete maths I did in my first year software engineering degree. lol good old days.

[frother]

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.

[davidrosenman]

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.✨

[HenryGhoul]

Which is the formula that puts uses the magnitudes?

[richavajpayee]

length of vector is magnitude of vector. correct ?

[inthebackwiththerabbish]

4:54 lmao nope taking it at a college level degree 😂

[suhailbhat]

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.

[JoffreyB]

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