Answer
-47
Work Step by Step
We calculate the determinant as follows:
det $\begin{pmatrix}u\\v\\w\end{pmatrix}=\begin{vmatrix}6&-1&2\\1&2&4\\1&0&-3\end{vmatrix}$
$=6(2(-3)-4\times0)+1(1(-3)-4\times1)+2(1\times0-2\times1)$
$= -36-7-4=-47$