Answer
$(-2,8,5).$
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, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
$u×v$ is the determinant of the matrix $\begin{bmatrix}
i& j & k \\
4& 1&0\\
3&2 &-2 \\
\end{bmatrix}
$
Thus $u×v=(-2,8,5).$
$(-2,8,5)(4,1,0)=-8+8+0=0$,
$(-2,8,5)(3,2,-2)=-6+16-10=0$, thus it is orthogonal to both $u$ and $v$
