Answer
$6$
Work Step by Step
We know that $ai+bj+ck=(a,b,c).$
We know that for a matrix
$
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
$
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
$v×w$ is the determinant of the matrix $\begin{bmatrix}
i& j & k \\
3& -2&1\\
2&-3 &-2 \\
\end{bmatrix}
$
Thus $v×w=(7,8,-5).$
Thus $u\cdot (v\times w)=(-2,1,0)(7,8,-5)=-14+8+0=-6$
Thus,
Area$=|u\cdot (v\times w)|=|-6|=6$
