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Section B.1 Hodge Dual
Identity B.1.1 . The Cross Product as a Dual Wedge Product.
In Clifford algebra \(\mathcal{Cl}(0,3)\) (Euclidean 3-D space), the standard vector cross product $\vec{a}\times\vec{b}$ is equivalent to the dual of the geometric wedge product $\vec{a}\wedge\vec{b}$ as follows:
\begin{equation*}
\vec{a}\times\vec{b} = \vec{a}\wedge\vec{b}\mathcal{I}^{-1}
\end{equation*}
where \(\mathcal{I}=\mathbf{e}_1\mathbf{e}_2\mathbf{e}_3\) is the unit pseudoscalar in \(\mathcal{Cl}(0,3)\text{.}\)
