If \( \vec{A}+\vec{B} \) is a unit vector along \( \mathrm{x} \)-ax...

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If \( \vec{A}+\vec{B} \) is a unit vector along \( \mathrm{x} \)-axis and \( \vec{A}=\hat{i}-\hat{j}+\hat{k} \), then what is \( \vec{B} \) ?
(1) \( \hat{j}+\hat{k} \)
(2) \( \hat{j}-\hat{k} \)
(3) \( \hat{i}+\hat{j}+\hat{k} \)
(4) \( \hat{i}+\hat{j}-\hat{k} \)
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