Answer
$(-2,-1,1).$
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& -1&1\\
0&1 &1 \\
\end{bmatrix}
$
Thus $u×v=(-2,-1,1).$
$(-2,-1,1)(1,-1,1)=-2+1+1=0$,
$(-2,-1,1)(0,1,1)=0-1+1=0$,
thus it is orthogonal to both $u$ and $v$ (two vectors are perpendicular if their dot product is $0$).
