If a and b are the vectors AB and BC determined by the adjacent sides of a ragular hexagon. What are the vectors determined by the other sides taken is order?

Explanation

To solve the problem, we need to determine the vectors corresponding to the sides of a regular hexagon, given that vectors \( \mathbf{a} \) and \( \mathbf{b} \) represent the vectors \( \overrightarrow{AB} \) and \( \overrightarrow{BC} \) respectively.

### Step-by-Step Solution:

1. **Understanding the Hexagon Structure**:
- A regular hexagon has six sides and can be visualized with vertices labeled as \( A, B, C, D, E, F \).
- The sides of the hexagon can be represented as vectors based on the adjacent vertices.

...