Answer
47
Work Step by Step
We calculate the dot product and cross product using the determinant as follows:
$\textbf{v}\cdot (\textbf{u}\times\textbf{w})=$ det $\begin{pmatrix}\textbf{v}\\\textbf{u}\\\textbf{w}\end{pmatrix}$
$=\begin{vmatrix}1&2&4\\6&-1&2\\1&0&-3\end{vmatrix}$
$=1((-1\times-3)-2\times0)-2((6\times-3)-2\times1)+4(6\times0-1\times-1)$
$=3+40+4=47$
