If a = i +2 k, b = i + j + k, c =7 i -3 j +4 k, r × b + b × c = 0 and r · a =0. Then r · c is equal to

If $\displaystyle \vec{a}=\hat{i}+2 \hat{k}, \vec{b}=\hat{i}+\hat{j}+\hat{k}, \vec{c}=7 \hat{i}-3 \hat{j}+4 \hat{k}, \vec{r} \times \vec{b}+\vec{b} \times \vec{c}=\overrightarrow{0}$ and $\displaystyle \vec{r} \cdot \vec{a}=0$. Then $\displaystyle \vec{r} \cdot \vec{c}$ is equal to