Find the distance of the point $(1, -2, 9)$ from the point of intersection of the line $\vec{r} = 4\hat{i} + 2\hat{j} + 7\hat{k} + \lambda$3\hat{i} + 4\hat{j} + 2\hat{k}$$ and the plane $\vec{r} \cdot $\hat{i} - \hat{j} + \hat{k}$ = 10$.