A non-zero vector \( \vec{a} \) is parallel to the line of intersection of the plane determined ...

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A non-zero vector \( \vec{a} \) is parallel to the line of intersection of the plane determined by the vectors \( \hat{i}, \hat{i}+\hat{j} \) and the plane determined by the vectors \( \hat{i}-\hat{j}, \hat{i}+\hat{k} \). The angle between \( \vec{a} \) and the vector \( \hat{i}-2 \hat{j}+2 \hat{k} \) is
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