In case of a projectile, where is the angular momentum minimum

The correct answer is: At the starting point

Let us analyze the angular momentum of a projectile during its motion.
The angular momentum $L$ of a particle of mass $m$ with position vector $r$ and velocity vector $v$ relative to the point of projection (the starting point) is defined as:
$L=r\times p=m(r\times v)$

At the starting point (the point of projection), the position vector of the projectile with respect to itself is:
$r=0$
Therefore, substituting $r=0$ into the expression for angular momentum gives:
$L=0$

At any other point during the flight, both the position vector $r$ and velocity vector $v$ are non-zero, and they are not parallel (except potentially at the exact start, but there $r=0$ anyways). As a result, the cross product is non-zero, making the angular momentum greater than zero.

Thus, the magnitude of angular momentum is minimum (specifically, zero) at the starting point.