A line passing through the points $\text{A}(1, 2, 3)$ and $\text{B}(5, 8, 11)$ intersects the line $\vec{r} = 4\hat{i} + \hat{j} + \lambda$5\hat{i} + 2\hat{j} + \hat{k}$$. Find the co-ordinates of the point of intersection. Hence, write the equation of a line passing through the point of intersection and perpendicular to both the lines.