we have to use calculate using right hand coordinate.
xudongw
I think why it only work in 3D is that for higher dimensions, say 4D, what orthogonal to both vectors will be a plane, instead of a vector.
motoole2
That's right; computing the cross product of u x v in 4D doesn't really make sense, because there are many potential vectors that are orthogonal to both u and v.
alyssal
Is there any equivalent to the cross product in different dimensions?
motoole2
There are other cross-product-like operations, definitely. For example, if you have three vectors in 4D space, once could compute a fourth vector that is orthogonal to those first three vectors. More specifically, you can think of the Hodge star as a generalization of cross products (though this is outside the scope of this class).
we have to use calculate using right hand coordinate.
I think why it only work in 3D is that for higher dimensions, say 4D, what orthogonal to both vectors will be a plane, instead of a vector.
That's right; computing the cross product of
u x vin 4D doesn't really make sense, because there are many potential vectors that are orthogonal to bothuandv.Is there any equivalent to the cross product in different dimensions?
There are other cross-product-like operations, definitely. For example, if you have three vectors in 4D space, once could compute a fourth vector that is orthogonal to those first three vectors. More specifically, you can think of the Hodge star as a generalization of cross products (though this is outside the scope of this class).