Let \( \vec{a} = \hat{i} + \hat{j} + 2\hat{k} \) and \( \vec{b} = -\hat{i} + 2\hat{j} + 3\hat{k} \). Then the vector product \( (\vec{a} + \vec{b}) \times \big((\vec{a} \times ((\vec{a} - \vec{b}) \times \vec{b})\times\vec b\big) \) is equal to:
\( 5\,(34\hat{i} - 5\hat{j} + 3\hat{k}) \)
\( 5\,(30\hat{i} - 5\hat{j} + 7\hat{k}) \)
\( 7\,(34\hat{i} - 5\hat{j} + 3\hat{k}) \)
