Answer
$25$
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
\]
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
We know that if we have two vectors $v=ai+bj+ck$ and $w=di+ej+fk$, then $v\times w$ can be obtained by the determinant of: \[
\left[\begin{array}{rrr}
i & j & k \\
a &b & c \\
d &e & f \\
\end{array} \right]
\]
Hence here $D=v\times u=i(3\cdot1-2\cdot(-3))-j((-3)\cdot1-2\cdot2)+k((-3)\cdot(-3)-3\cdot2)=9i+7j+3k.$
$(v\times u)\cdot w=(9i+7j+3k)(i+j+3k)=(9)(1)+(7)(1)+(3)(3)=9+7+9=25$
