9 The planes \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\) have vector equations $$\mathbf { r } = \lambda _ { 1 } ( \mathbf { i } + \mathbf { j } - \mathbf { k } ) + \mu _ { 1 } ( 2 \mathbf { i } - \mathbf { j } + \mathbf { k } ) \quad \text { and } \quad \mathbf { r } = \lambda _ { 2 } ( \mathbf { i } + 2 \mathbf { j } + \mathbf { k } ) + \mu _ { 2 } ( 3 \mathbf { i } + \mathbf { j } - \mathbf { k } )$$ respectively. The line \(l\) passes through the point with position vector \(4 \mathbf { i } + 5 \mathbf { j } + 6 \mathbf { k }\) and is parallel to both \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\). Find a vector equation for \(l\). Find also the shortest distance between \(l\) and the line of intersection of \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\).