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

Explanation

To solve the problem of determining the vectors for the sides of a regular hexagon given vectors \( \mathbf{a} \) and \( \mathbf{b} \) for adjacent sides \( AB \) and \( BC \), we can follow these steps:

### Step 1: Understand the Geometry of the Hexagon
A regular hexagon has six sides, and the vectors for these sides can be derived from the given vectors \( \mathbf{a} \) (for side \( AB \)) and \( \mathbf{b} \) (for side \( BC \)). The sides of the hexagon are connected in a cyclic manner.

### Step 2: Identify the Vectors for Each Side
1. **Vector \( \mathbf{a} \)**: This is the vector for side \( AB \).
2. **Vector \( \mathbf{b} \)**: This is the vector for side \( BC \).
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