If $\overline{\mathrm{a}}=2\overline{\mathrm{i}}+\overline{\mathrm{k}},\overline{\mathrm{b}}=\overline{\mathrm{i}}+\overline{\mathrm{j}}+\overline{\mathrm{k}}, \overline{\mathrm{c}}=4\overline{\mathrm{i}}-3\overline{\mathrm{j}}+7\overline{\mathrm{k}}$ then the vector $\overline{\mathrm{r}}$ satisfying $\overline{\mathrm{r}}\times \overline{\mathrm{b}}=\overline{\mathrm{c}}\times \overline{\mathrm{b}}$ and $\overline{\mathrm{r}}.\overline{\mathrm{a}}=0$ is

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