Answer
$(1,3,1).$
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 \\
2& -1&1\\
3&-1 &0 \\
\end{bmatrix}
$
Thus $u×v=(1,3,1).$
$(1,3,1)(2,-1,1)=2-3+1=0$,
$(1,3,1)(3,-1,0)=3-3+0=0$, thus it is orthogonal to both $u$ and $v$
