  In this paper we use a generalized vector product to construct an exterior
form $\wedge :(\mathbb{R}^{n}) ^{k}\to \mathbb{R}^{\binom{n}{k}}$, where
$\binom{n}{k}=\frac{n!}{(n-k)!k!}$, $k\leq n$. Finally, for $n=k-1$ we
introduce the reversing operation to study this generalized vector product over
palindromic and antipalindromic vectors.
