TeX Quellcode:

\begin{matrix}\vec{a}^{\,T} \cdot \left(\vec{b} \times \vec{c}\right) &=& \begin{pmatrix}-21;\,6;\,-35\end{pmatrix} \cdot \left(\begin{pmatrix}-7\cr-18\cr28\end{pmatrix} \times \begin{pmatrix}-7\cr6\cr16\end{pmatrix}\right) \cr \cr &=& \begin{pmatrix}-21;\,6;\,-35\end{pmatrix} \cdot \begin{pmatrix}-18 \cdot 16 &-& 28 \cdot 6 \cr 28 \cdot (-7) &-& (-7) \cdot 16 \cr -7 \cdot 6 &-& (-18) \cdot (-7) \end{pmatrix} \cr \cr &=& \begin{pmatrix}-21;\,6;\,-35\end{pmatrix} \cdot \begin{pmatrix}-456\cr-84\cr-168\end{pmatrix} \cr \cr &=& -21 \cdot \left(-456\right) + 6 \cdot \left(-84\right) + \left(-35\right) \cdot \left(-168\right) &=& 14.952\end{matrix}