A vector a is parallel to the line of intersection of the plane determined by the vectors i, i + j and the plane determined by the vectors i - j, i +…

A vector $\displaystyle \vec{a}$ is parallel to the line of intersection of the plane determined by the vectors $\displaystyle \hat{i}, \hat{i}+\hat{j}$ and the plane determined by the vectors $\displaystyle \hat{i}-\hat{j}, \hat{i}+\hat{k}$. The obtuse angle between $\displaystyle \vec{a}$ and the vector $\displaystyle \vec{b}=\hat{i}-2 \hat{j}+2 \hat{k}$ is