TeX Quellcode:

\begin{matrix}\vec{a}^{\,T} \cdot \left(\vec{b} \times \vec{c}\right) &=& \begin{pmatrix}-25;\,4;\,1\end{pmatrix} \cdot \left(\begin{pmatrix}-36\cr\frac{12}{5}\cr-9\end{pmatrix} \times \begin{pmatrix}-10\cr11\cr\frac{3}{2}\end{pmatrix}\right) \cr \cr &=& \begin{pmatrix}-25;\,4;\,1\end{pmatrix} \cdot \begin{pmatrix}\frac{12}{5} \cdot \frac{3}{2} &-& (-9) \cdot 11 \cr -9 \cdot (-10) &-& (-36) \cdot \frac{3}{2} \cr -36 \cdot 11 &-& \frac{12}{5} \cdot (-10)\end{pmatrix} \cr \cr &=& \begin{pmatrix}-25;\,4;\,1\end{pmatrix} \cdot \begin{pmatrix}\frac{513}{5}\cr144\cr-372\end{pmatrix} \cr \cr &=& -25 \cdot \dfrac{513}{5} + 4 \cdot 144 + 1 \cdot \left(-372\right) &=& -2.361\end{matrix}