One neighboring state of the Vijayanagara Empire was the Bahmani Sultanate. It was located to the north of Vijayanagara and often engaged in military and diplomatic relations with the empire.
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?