axes of the angular
momentum 
of a particle,
whose position vector is 
with
components and momentum is 
with components 
and 
. Show that if the
particle moves only in the 
plane,
the angular momentum has only a z-component.
Answer:
We can write
and 
But 
or 
Comparing the coefficients of 
and 
on the two sides,
we get the components of 
as
follows:
and
If the particle is constrained
to move only in the 
plane,
then 
and 
. Hence
As only the unit vector k corresponding
to z-direction survives, the angular momentum has only a
z-component.
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