Let a = i +2 j + k, b =3 i -3 j +3 k, c =2 i - j +2 k and d be a vector such that b × d = c × d and a · d =4. Then |( a × d )|^2 is equal to ____.

Let $\displaystyle \vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}-3 \hat{j}+3 \hat{k}, \vec{c}=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\displaystyle \vec{d}$ be a vector such that $\displaystyle \vec{b} \times \vec{d}=\vec{c} \times \vec{d}$ and $\displaystyle \vec{a} \cdot \vec{d}=4$. Then $\displaystyle |(\vec{a} \times \vec{d})|^2$ is equal to $\displaystyle \_\_\_\_$.