Let a =√ 7 i + j - k and b = j +2 k. If r is a vector such that r × a + a × b = 0 and r · a =0, then |3 r |^2 is equal to:

Let $\displaystyle \vec{a}=\sqrt{7} \hat{i}+\hat{j}-\hat{k}$ and $\displaystyle \vec{b}=\hat{j}+2 \hat{k}$. If $\displaystyle \vec{r}$ is a vector such that $\displaystyle \vec{r} \times \vec{a}+\vec{a} \times \vec{b}=\overrightarrow{0}$ and $\displaystyle \vec{r} \cdot \vec{a}=0$, then $\displaystyle |3 \vec{r}|^2$ is equal to: