Identify the ancient dynasty with the help of the following information:
1. They issued spectacular gold coins.
2. Their history can be reconstructed through Prashastis.
3. Harisena was the court poet of one of its rulers.
If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?