Let a = i +4 j +2 k, b =3 i -2 j +7 k and c =2 i - j +4 k. If a vector d satisfies d × b = c × b and d · a =24, then | d |^2 is equal to

Let $\displaystyle \vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}$ and $\displaystyle \vec{c}=2 \hat{i}-\hat{j}+4 \hat{k}$. If a vector $\displaystyle \vec{d}$ satisfies $\displaystyle \vec{d} \times \vec{b}=\vec{c} \times \vec{b}$ and $\displaystyle \vec{d} \cdot \vec{a}=24$, then $\displaystyle |\vec{d}|^2$ is equal to