Answer
$(-8,-14,54)$
Work Step by Step
We know that for a matrix
$
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
$
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
$u\times v$ is the determinant of the matrix $\begin{bmatrix}
i & j& k \\
12&-3&1\\
-2&5&1\\
\end{bmatrix}
$
Thus $u\times v=(-8,-14,54)$
$(-8,-14,54)(12,-3,1)=-96+42+54=0$, $(-8,-14,54)(-2,5,1)=16-70+54$, thus it is orthogonal to both $u$ and $v$
