Find the components along the `x,y,z` axes of the angular momentum `overset rarr(L)` of a particle, whose position vector is `overset rarr(r )` with components `x,y,z` and momentum is `overset rarr(p)` with components `p_(x), p_(y) and p_(z)`. Show that if the particle moves only in the `x-y` plane, the angular momentum has only a z-component.

Explanation

To find the components of the angular momentum \(\vec{L}\) of a particle, we start with the definitions of the position vector \(\vec{r}\) and momentum vector \(\vec{p}\).

1. **Define the position and momentum vectors:**
\[ \vec{r} = x \hat{i} + y \hat{j} + z \hat{k} \]
\[
\vec{p} = p_x \hat{i} + p_y \hat{j} + p_z \hat{k}
...