TeX source:

\begin{array}{rcl} \vec{a}^{\,T}\cdot\left(\vec{b} \times \vec{c}\right) &=& \begin{pmatrix}2;\,-6;\,1\end{pmatrix}\cdot\left(\begin{pmatrix}5\cr-1\cr-10\end{pmatrix} \times \begin{pmatrix}-3\cr0\cr-1\end{pmatrix}\right) \cr &=& \begin{pmatrix}2;\,-6;\,1\end{pmatrix}\cdot\begin{pmatrix}-1\cdot \left(-1\right) - \left(-10\right)\cdot 0 \cr -10\cdot \left(-3\right) - 5\cdot \left(-1\right) \cr 5\cdot 0 - \left(-1\right)\cdot \left(-3\right)\end{pmatrix} \cr &=& \begin{pmatrix}2;\,-6;\,1\end{pmatrix}\cdot\begin{pmatrix}1\cr35\cr-3\end{pmatrix} \cr &=& 2\cdot 1 + \left(-6\right)\cdot 35 - 3 = -211 \end{array}