Let a be a non-zero vector parallel to the line of intersection of the two planes described by i + j, i + k and i - j, j - k. If θ is the angle…

Let $\displaystyle \vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\displaystyle \hat{i}+\hat{j}, \hat{i}+\hat{k}$ and $\displaystyle \hat{i}-\hat{j}, \hat{j}-\hat{k}$. If $\displaystyle \theta$ is the angle between the vector $\displaystyle \vec{a}$ and the vector $\displaystyle \vec{b}=2 \hat{i}-2 \hat{j}+\hat{k}$ and $\displaystyle \vec{a} \cdot \vec{b}=6$, then the ordered pair $\displaystyle (\theta,|\vec{a} \times \vec{b}|)$ is equal to