Let a =2 i +3 j +4 k, b = i -2 j -2 k and c =- i +4 j +3 k. If d is a vector perpendicular to both b and c, and a · d =18, then | a × d |^2 is equal…

Let $\displaystyle \vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}-2 \hat{k}$ and $\displaystyle \vec{c}=-\hat{i}+4 \hat{j}+3 \hat{k}$. If $\displaystyle \vec{d}$ is a vector perpendicular to both $\displaystyle \vec{b}$ and $\displaystyle \vec{c}$, and $\displaystyle \vec{a} \cdot \vec{d}=18$, then $\displaystyle |\vec{a} \times \vec{d}|^2$ is equal to