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 given its position vector \(\vec{r}\) and momentum \(\vec{p}\), we can follow these steps:

### Step 1: Define the Angular Momentum
The angular momentum \(\vec{L}\) of a particle is defined as:
\[ \vec{L} = \vec{r} \times \vec{p} \]
where \(\vec{r}\) is the position vector and \(\vec{p}\) is the momentum vector.
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