The position of a particle is given by : $\overrightarrow{r}=(\hat{i}+2\hat{j}-\hat{k})$  and momentum $\overrightarrow{P}=(3\widehat{i}+4\widehat{j}-2\widehat{k})$ . The angular momentum is perpendicular to

$\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}=\left|\begin{array}{rrr}\hat{i}& \hat{j}& \hat{k}\\ 1& 2& -1\\ 3& 4& -2\end{array}\right|$
$=0\widehat{i}-\widehat{j}-2\widehat{k}=-\widehat{j}-2\widehat{k}$ and the X- axis is given by $i+0\widehat{j}+0\widehat{k}$ Dot product of these two vectors is zero i.e. angular momentum is perpendicular to X-axis.