Show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the motion.

(N/A) Let the particle with mass $m$ and velocity $v$ be at point $P$ at some instant $t$. We want to calculate the angular momentum of the particle about an arbitrary point $O$.
The angular momentum is given by $l = r \times mv$. Its magnitude is $mvr \sin \theta$,where $\theta$ is the angle between $r$ and $v$ as shown in the figure.
Although the particle changes position with time,the line of direction of $v$ remains the same. The perpendicular distance from $O$ to the line of motion of the particle is $d = r \sin \theta$,which is a constant.
Further,the direction of $l$ is perpendicular to the plane containing $r$ and $v$. This direction does not change with time. Thus,$l$ remains the same in magnitude and direction and is therefore conserved.