Find the Cartesian as well as the vector equation of the plants passing through the intersection of the plants $\overset \rightharpoonup {r}. (2 \hat{i} + 6 \hat{j}) + 12 = 0$ and $\overset \rightharpoonup {r}. (3 \hat{i} - \hat{j} + 4 \hat{k}) = 0$. Which are at unit distance from the origin?