Answer
$(13,6,-1).$
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 \\
0& 1&6\\
1&-2 &1 \\
\end{bmatrix}
$
Thus $u×v=(13,6,-1).$
$(13,6,-1)(0,1,6)=0+6-6=0$,
$(13,6,-1)(1,-2,1)=13-12-1=0$,
thus it is orthogonal to both $u$ and $v$ (two vectors are perpendicular if their dot product is $0$).
