Complete the following ionic equations:
$5\text{SO}_3^{2-} + 2\text{MnO}_4^{-} + 6\text{H}^+ \longrightarrow$
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?