TeX Quellcode:

\begin{matrix}\vec{a}^{\,T} \cdot \left(\vec{b} \times \vec{c}\right) &=& \begin{pmatrix}1;\,-1;\,2\end{pmatrix} \cdot \left(\begin{pmatrix}10\cr0\cr-8\end{pmatrix} \times \begin{pmatrix}4\cr-5\cr0\end{pmatrix}\right) \cr \cr &=& \begin{pmatrix}1;\,-1;\,2\end{pmatrix} \cdot \begin{pmatrix}0 \cdot 0 &-& (-8) \cdot (-5) \cr -8 \cdot 4 &-& 10 \cdot 0 \cr 10 \cdot (-5) &-& 0 \cdot 4 \end{pmatrix} \cr \cr &=& \begin{pmatrix}1;\,-1;\,2\end{pmatrix} \cdot \begin{pmatrix}-40\cr-32\cr-50\end{pmatrix} \cr \cr &=& 1 \cdot \left(-40\right) + \left(-1\right) \cdot \left(-32\right) + 2 \cdot \left(-50\right) &=& -108\end{matrix}