Answer
$(-2,3,-1).$
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 \\
1& 1&1\\
2&1 &-1 \\
\end{bmatrix}
$
Thus $u×v=(-2,3,-1).$
$(-2,3,-1)(1,1,1)=-2+3-1=0$,
$(-2,3,-1)(2,1,-1)=-4+3+1=0$, thus it is orthogonal to both $u$ and $v$
