Show that if the particle moves only in x-y plane the angular momentum has only a z component

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Q. Find the components along the x, y, z axes of the angular momentum

l

of a particle, whose position vector is

r

with components x, y, z and momentum is

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.

Q. If a particle moves in the x-y plane, the resultant angular momentum has

Find the components along the x, y, z axes of the angular momentum l of a particle, whose position vector is r with components x, y, z and momentum is 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.