Answer
$0\hat{i}+0\hat{j}+0\hat{k}$ or, $\lt 0,0,0 \gt$
Work Step by Step
Let us consider $u=\lt -2,3,4 \gt$ and $v=\lt \dfrac{1}{6},\dfrac{-1}{4},\dfrac{-1}{3} \gt$
Now,
$\hat{n}=u \times v=\begin{vmatrix}i&j&k\\-2&3&4\\\dfrac{1}{6}&\dfrac{-1}{4}&\dfrac{-1}{3}\end{vmatrix}$
or, $u \times v=[3(\dfrac{-1}{3})-4(\dfrac{-1}{4})] i+[(4)(\dfrac{1}{6})-(-2)(\dfrac{-1}{3})]j+[ -2(\dfrac{-1}{4})-3(\dfrac{1}{6})]k$
or, $u \times v=(-1+1)i+(\dfrac{-2}{3}+\dfrac{2}{3})j+( \dfrac{1}{2}-\dfrac{1}{2}) k$
Thus, $u \times v=0\hat{i}+0\hat{j}+0\hat{k}$
