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