Let \( \vec{a} = \hat{i} + \hat{j} - \hat{k} \) and \( \vec{c} = 2\hat{i} - 3\hat{j} + 2\hat{k} \). Then the number of vectors \( \vec{b} \) such that \( \vec{b} \times \vec{c} = \vec{a} \) and \( |\vec{b}| \in \{1,2,\ldots,10\} \) is:
\( 0 \)
\( 1 \)
\( 2 \)
\( 3 \)
