As a projectile thrown upward moves in its parabolic path, at what point along its path are the velocity and acceleration vectors for the projectile perpendicular to each other

Maximum height

Explanation:

Suppose a projectile is thrown at an angle of with velocity u

As the projectile moves upward, its vertical component of velocity decreases due to gravity. While the horizontal component remains the same as there is no acceleration in the horizontal direction.  

At maximum height vertical component of velocity is zero. At this instant horizontal component of velocity is perpendicular to the acceleration due to gravity. This can be explained with the diagram.