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

`l_(z)=xp_(y)-yp_(x),l_(x)=yp_(z)-zp_(y),l_(y)=zp_(x)-xp_(z)`