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Let \( \vec{a}=\hat{j}-\hat{k} \) and \( \vec{c}=\hat{i}-\hat{j}-\hat{k} \). Then the vector \( \vec{b} \) satisfying \( \vec{a} \times \vec{b}+\vec{c}=0 \) and \( \vec{a} \cdot \vec{b}=3 \) is
(A) \( \hat{i}+\hat{j}-2 \hat{k} \)
(B) \( -\hat{i}+\hat{j}-2 \hat{k} \)
(C) \( 2 \hat{i}-\hat{j}+2 \hat{k} \)
(D) \( \hat{i}-\hat{j}-2 \hat{k} \)
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