Suppose we have a vector $(a,b)$ in $2$-space. Then the vector $(-b,a)$ is orthogonal to the one we started with. Furthermore, the function $$(a,b) \mapsto (-b,a)$$ is linear.
Suppose instead we have ...
We know how to make cross product of three dimensional vectors.
$$ \vec A \times \vec B = \vec C$$
$ \vec A = (A_i; A_j; A_k)$
$ \vec B = (B_i; B_j; B_k)$
$ \vec C = (C_i; C_j; C_k)$
$C_i = \...
Why the cross product between 2 (two!) vectors exists only in 3 dimensions?
The article "Cross Products of Vectors in Higher Dimensional Euclidean Spaces" by W. M. Massey (see http://doi.org/10.2307/...