Answer
$\frac{(1,-2,-2)}{3}$
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, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
A vector orthogonal to $u$ and $v$ is $u\times v$.
$u×v$ is the determinant of the matrix $\begin{bmatrix}
i& j & k \\
2& -3&4\\
0&-1 &1 \\
\end{bmatrix}
$
Thus $u×v=(1,-2,-2).$
And a unit vector parallel to this is: $\frac{u\times v}{|u\times v|}=\frac{(1,-2,-2)}{\sqrt{1^2+(-2)^2+(-2)^2}}=\frac{(1,-2,-2)}{\sqrt{9}}=\frac{(1,-2,-2)}{3}$
