TeX Quellcode:

\begin{matrix}\vec{a}^{\,T} \cdot \left(\vec{b} \times \vec{c}\right) &=& \begin{pmatrix}37;\,7;\,-32\end{pmatrix} \cdot \left(\begin{pmatrix}-30\cr-5\cr13\end{pmatrix} \times \begin{pmatrix}-10\cr-45\cr-48\end{pmatrix}\right) \cr \cr &=& \begin{pmatrix}37;\,7;\,-32\end{pmatrix} \cdot \begin{pmatrix}-5 \cdot (-48) &-& 13 \cdot (-45) \cr 13 \cdot (-10) &-& (-30) \cdot (-48) \cr -30 \cdot (-45) &-& (-5) \cdot (-10)\end{pmatrix} \cr \cr &=& \begin{pmatrix}37;\,7;\,-32\end{pmatrix} \cdot \begin{pmatrix}825\cr-1.570\cr1.300\end{pmatrix} \cr \cr &=& 37 \cdot 825 + 7 \cdot \left(-1.570\right) + \left(-32\right) \cdot 1.300 &=& -22.065\end{matrix}