Vector Algebra

If $\bar{p}=2 \hat{i}+\hat{k}, \bar{q}=\hat{i}+\hat{j}+\hat{k}, \bar{r}=4 \hat{i}-3 \hat{j}+7 \hat{k}$ and a vector $\overline{\mathrm{m}}$ is such that $\overline{\mathrm{m}} \times \overline{\mathrm{q}}=\overline{\mathrm{r}} \times \overline{\mathrm{q}}, \overline{\mathrm{m}} \cdot \overline{\mathrm{p}}=0$, then $\overline{\mathrm{m}}=\ldots$.