3 The lines \(l _ { 1 }\) and \(l _ { 2 }\) have equations \(\mathbf { r } = 6 \mathbf { i } + 2 \mathbf { j } + 7 \mathbf { k } + \lambda ( \mathbf { i } + \mathbf { j } )\) and \(\mathbf { r } = 4 \mathbf { i } + 4 \mathbf { j } + \mu ( - 6 \mathbf { j } + \mathbf { k } )\) respectively. 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 \(l _ { 2 }\). Find the position vectors of \(P\) and \(Q\).

3 The lines $l _ { 1 }$ and $l _ { 2 }$ have equations $\mathbf { r } = 6 \mathbf { i } + 2 \mathbf { j } + 7 \mathbf { k } + \lambda ( \mathbf { i } + \mathbf { j } )$ and $\mathbf { r } = 4 \mathbf { i } + 4 \mathbf { j } + \mu ( - 6 \mathbf { j } + \mathbf { k } )$ respectively. 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 $l _ { 2 }$. Find the position vectors of $P$ and $Q$.\\

\hfill \mbox{\textit{CAIE FP1 2019 Q3}}