By definition of angular momentum

$\vec{l}=\vec{r} \times \vec{p}$

$\hat{i}\hat{j}\hat{k}$

$x\;y\;z$

$\mathrm{P}_{x}\mathrm{P}_{y}\mathrm{P}_{z}$

$=\hat{i}[y \mathrm{P} z-z \mathrm{P} y]+\hat{j}[z \mathrm{P} x-x \mathrm{P} z]+\hat{k}[x \mathrm{P} y-y \mathrm{P} x] \ldots \ldots . .(1)$

$\therefore \vec{l}=l_{x} \hat{i}+l_{y} \hat{j}+l_{z} \hat{k}$

Here $l_{x}, l_{y}$ and $l_{z}$ are the components of $\vec{l}$ along $\mathrm{X}, \mathrm{Y}$ and $Z$ axis respectively.