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]