Answer
$(-1,-1,-1).$
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, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
$u×v$ is the determinant of the matrix $\begin{bmatrix}
i& j & k \\
2& -3&1\\
1&-2 &1 \\
\end{bmatrix}
$
Thus $u×v=(-1,-1,-1).$
$(-1,-1,-1)(2,-3,1)=-2++3-1=0$,
$(-1,-1,-1)(1,-2,1)=-1+2-1=0$, thus it is orthogonal to both $u$ and $v$
