Describing rotation in 3d with a vector

Learn how a three-dimensional vector can be used to describe three-dimensional rotation. This is important for understanding three-dimensional curl.

[neopalm]

It's official. Khanacademy has been graced with the presence of a pi creature. Grant has fully joined team Khan.

[frognik]

Came here (and elsewhere) after watching a Quaternions numberphile video saying you need 4 dimensions to describe 3 dimensional rotation, 1 scalar + 3 vector.
The right hand rule + vector magnitude is a really smart idea for getting the scalar inherently.

[jvcmarc]

3blue1brown is slowly taking over KhanAcademy

[Rocky-mecw]

π creatures are now on khan academy too.

#πFever

[ONS]

The pi creature coupled with Grant's voice literally made me think I was watching 3blue1brown videos. I didn't realize this was Khan until the video ended.

[namitanene]

The pi creature looks so cute when its rotating 😣✊

[vigneshwarm]

Ah! I can finally see the pi creatures in Khan Academy.

[zts]

Great videos. They are wonderful conceptual understandings for the intuition behind the mechanics. Are you the same mind behind 3blue1brown ? voice and style are nearly identical. And if yes, when did you jump on the Khan team ?

[janApen]

I love you! ... I.. I mean I love your math.

[huyngo]

That convention resembles the right hand rule in electromagnetic.

[shenelf]

it is like that curl3D(x, y, z) = (curl2D(yz), curl2D(zx), curl2D(xy))

[Magnawulf]

Is it really possible to describe all rotations in 2D with one number? Aren't you also forgetting about the center of origin of the rotation? That's not convention, it's something that can vary. It doesn't seem possible to map every point to it's rotated image using one number (theta in your case), you would need a two dimensional number like a vector right? Similarly wouldn't you need a 3 dimensional number to talk about rotation in 3d?

[roygalaasen]

I know Grant has been doing videos with Khan Academy before, and I was sure that I was watching Khan Academy, but when the pi figure appeared spinning around on my screen I had to double check that I hadn’t actually stumbled onto 3b1b channel instead.

[joschistep]

1:53 so now it's official.
It really doesn't matter.

[diqnu]

@Khan Academy: I´m confused with one thing: We are able to describe a rotation (spin) by a vector of course. But adding two of them will result in one new single-axis spin representation. Though: This can´t be right: A 1-Hz-spin around the x-axis combined with a 10-Hz-spin around z-axis is definitely not the same as single-axis rotation around (1, 0, 100), is it?
So, spin vestors aren´t real vectors in the sense of a vector space? How are multi-axes spins descibed mathematically then?

[giridharpalvai]

Rotation is always up word direction ?

[feiwang]

ha this π comes from the videos from 3 blue 1 brown =D

[giridharpalvai]

I am learning cmm machine possible to give rotation and transaction topics information

[jj]

I was 3 min through the video considering its 3blue1brown channel lol

[aienbalosaienbalos]

To use a vector, you are limiting yourself to rotations in 3D, because only then is the normal of the plane of rotation a vector.

Furthermore, the rotation is on a plane, why would it's definition involve a vector in a other, unrelated dimension?


Which is why, in my opinion, and I think the opinion of most people that have heard of geometric algebra, it makes more sense to define the plane of rotation. To define a plane you would need 2 numbers, leaving the third number for the speed of rotation.

In some contexts, an oriented plane with a magnitude is called a bivector.

If you are interested, search a quick video about geometric algebra and bivectors.