2003 TYS

Referred to the origin $O$ , the position vectors of points $A$ and $B$ are $4\mathbf{i}-11\mathbf{j}+4\mathbf{k}$ and $7\mathbf{i}+\mathbf{j}+7\mathbf{k}$ respectively.

1. Find a vector equation for the line $l$ passing through $A$ and $B$ .[2]
2. Find the position vector of the point $P$ on $l$ such that $OP$ is perpendicular to $l$.[4]