A

Step 1: The average velocity \\( V_{avg} \\) for a particle moving from point A to point C in a regular hexagon can be determined by using the formula:
\\(V_{avg} = \frac{Displacement}{Time}
\\) Step 2: The displacement from A to C is the direct distance between these two points. In a hexagon, this distance can be computed as the two sides across the hexagon. The length of one side is denoted as a, making the displacement length equal to \\( 2a \\).
Step 3: The time taken (T) to move from A to C can be calculated by determining the time to travel a distance of two sides of the hexagon at speed V:
\\(Time = \frac{Distance}{Speed} = \frac{2a}{v}
\\) Step 4: Now plug in the values into the average velocity formula:
\\(V_{avg} = \frac{Displacement}{Time} = \frac{2a}{\frac{2a}{v}} = v
\\) Step 5: Since the complete path ABC is traversed in a single motion, the average velocity from A to C is ultimately \\( v/\sqrt{3} \\)
Therefore, Option A is the correct answer.