Answer
$2$
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 \\
-1& -1&0\\
3&4 &-1 \\
\end{bmatrix}
$
Thus $v×w=(1,-1,-1).$
Thus $u\cdot (v\times w)=(1,2,1)(1,-1,-1)=1-2-1=-2$
Thus Area$=|u\cdot (v\times w)|=|-2|=2$
