By far one of the best Math channels (and in my opinion recourses in general) out there. Thank you for your efforts. Keep it up
@Hold_it
2 жыл бұрын
Oooh, now it makes finally sense why the length gives us the area of the Parallelogramm. I just got told that it works, but i didn't see why it makes sense geometrically. The connection was so random for me. Thank you!
@malawigw
2 жыл бұрын
I will cross my fingers for this video
@paominlienguite2397
2 жыл бұрын
My favourite channel 😍😍😍
@thiloherold7087
2 жыл бұрын
Hi, As always a brilliant video! But one question arises while watching, why does this only work in R^3? In other words: what makes this space so different from R^2, R^4 or R^42? Thank you in advance!
@brightsideofmaths
2 жыл бұрын
We can discuss this in more detail later. However, the orthogonality property cannot be true in R^2 or R^4 as you maybe can visualize.
@nathanwycoff4627
2 жыл бұрын
@@brightsideofmaths I would just like to second this question; I'm also super curious if there are higher dimensional analogues :)
@brightsideofmaths
2 жыл бұрын
@@nathanwycoff4627 Yeah, there are but not as a product with two factors like here. We will discuss it later :)
@thegoofiestgoooberr
11 ай бұрын
@@nathanwycoff4627the only analogue i know of is in 7 dimensions
@andrewxiwu
2 жыл бұрын
As a way to remember this, wouldn't it be nice to point out that component 1 is the determinant of row2+row3? (and similar for other components) :). Of course, this determinant thing will happen again and again in later studies
@brightsideofmaths
2 жыл бұрын
Of course, the determinant we will cover soon :)
@rafaelschipiura9865
Жыл бұрын
I don't like this way of explaining it because it makes it look like the cross product can be extended to R^n with n different from 3.
@Independent_Man3
2 жыл бұрын
Hello, I live in a slightly noisy environment. Can you please increase your mic volume in future videos? I like watching your videos.
@brightsideofmaths
2 жыл бұрын
This is something KZitem should do automatically. Is it much quieter than other videos?
@Independent_Man3
2 жыл бұрын
@@brightsideofmaths Right after your video, I watched this video kzitem.info/news/bejne/t3l-rHeOoIuVqY4 and the sound was much louder. Just to give an example. If you can make it louder without much effort, then great. Otherwise, no problem.
@brightsideofmaths
2 жыл бұрын
@@Independent_Man3 I cannot reproduce this effect. Sorry. Maybe you try another browser?
@brightsideofmaths
2 жыл бұрын
@@Independent_Man3 Yeah, both videos have exactly the same loudness for my computer.
@notu483
Жыл бұрын
It is possible to turn on the captions to read the text rather than listening to it. This is a useful tool to watch these videos even within a noisy environment.
@ChrisOffner
2 жыл бұрын
The one thing that every single video on the cross product, including this one, seems to omit, is how to connect the algebraic formula/definition to a geometric intuition, i.e. *why* (in a geometric sense) does this algebraic definition result in a vector that's perpendicular to *u* and *v* and whose length matches the area of the parallelogram? The same goes for introductions of the determinant: *Why* (in a geometric sense) does the algebraic definition of the determinant of a matrix M give us the volume of the paralellepiped to which which the unit hypercube is mapped by the linear map encoded in M?
@brightsideofmaths
2 жыл бұрын
True! I want to cover this in general when we talk about the determinant. However, it felt wrong not to define the cross product early.
@ChrisOffner
2 жыл бұрын
@@brightsideofmaths Would be wonderful if you could cover it! Thank you, I greatly enjoy your videos. :)
@brightsideofmaths
2 жыл бұрын
@@ChrisOffner I have already some videos about the determinant in German. However, the English ones will be even better because it's embedded in the whole Linear Algebra series then :)
@Hold_it
2 жыл бұрын
@@brightsideofmaths Oh, that would be great. I always wondered why the cross product works :)
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