Answer
$0$
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 $D=v\times w=i(3\cdot3-2\cdot1)-j((-3)\cdot3-2\cdot1)+k((-3)\cdot1-3\cdot1)=7i+11j-6k.$
$v\cdot(v\times w)=(-3i+3j+2k)(7i+11j-6k)=(-3)7+3(11)+2(-6)=-21+33+(-12)=0$
