Also I believe you can take a cross product in 4D, but there's no way of determining which of the other 2 directions it points in.
coolbreeze
I think there could be cross product in higher dimension. This is related to how we define cross product. For example. In a 4D space, we can take three vectors and generate a vector which is orthogonal to those three vectors. If we only want two vectors, as this is a 'product' between two vectors, then there should be only the 3D version.
haotingl
Because our physical space is in 3d and it is very difficult for us human to imagine a 4d space
notme
A different right hand rule that I had learned in a class is instead of the fingers, you curl your right hand from u to v and stick your thumb up, and your thumb will point towards uxv. This helps me when I mess the fingers up.
mateib
Why is the octopus here
The poor guy has no right hand :(
I think there could be cross product in higher dimension. This is related to how we define cross product. For example. In a 4D space, we can take three vectors and generate a vector which is orthogonal to those three vectors. If we only want two vectors, as this is a 'product' between two vectors, then there should be only the 3D version.
Would it be possible to obtain these via a similar algorithm to the determinant one for the 3d cross product?
alexz2
I believe that we can compute the value for cross product for 3D or above, but it loses the geometric meaning
achekuri
My thought is that while the cross product can be taken in higher dimensions, semantically it means nothing in geometry and also it requires more vectors maybe? Like 4d cross product requires 3 vectors?
Kevinzzz
It's the only way to visualize cross product(in my opinion
atomicapple0
cute octopus
bokangw
For 2d there is no vector's direction orthogonal to both vector
Why is the octopus here
Also I believe you can take a cross product in 4D, but there's no way of determining which of the other 2 directions it points in.
I think there could be cross product in higher dimension. This is related to how we define cross product. For example. In a 4D space, we can take three vectors and generate a vector which is orthogonal to those three vectors. If we only want two vectors, as this is a 'product' between two vectors, then there should be only the 3D version.
Because our physical space is in 3d and it is very difficult for us human to imagine a 4d space
A different right hand rule that I had learned in a class is instead of the fingers, you curl your right hand from u to v and stick your thumb up, and your thumb will point towards uxv. This helps me when I mess the fingers up.
The poor guy has no right hand :(
Would it be possible to obtain these via a similar algorithm to the determinant one for the 3d cross product?
I believe that we can compute the value for cross product for 3D or above, but it loses the geometric meaning
My thought is that while the cross product can be taken in higher dimensions, semantically it means nothing in geometry and also it requires more vectors maybe? Like 4d cross product requires 3 vectors?
It's the only way to visualize cross product(in my opinion
cute octopus
For 2d there is no vector's direction orthogonal to both vector