9231 P11 - Jun 2011 - Q6 - 9 marks
6481
The line \(l_{1}\) passes through the point with position vector \(8 \mathbf{i}+8 \mathbf{j}-7 \mathbf{k}\) and is parallel to the vector \(4 \mathbf{i}+3 \mathbf{j}\). The line \(l_{2}\) passes through the point with position vector \(7 \mathbf{i}-2 \mathbf{j}+4 \mathbf{k}\) and is parallel to the vector \(4 \mathbf{i}-\mathbf{k}\). The point \(P\) on \(l_{1}\) and the point \(Q\) on \(l_{2}\) are such that \(P Q\) is perpendicular to both \(l_{1}\) and \(l_{2}\). In either order,
(i) show that \(P Q=13\),
(ii) find the position vectors of \(P\) and \(Q\).
