Referred to a fixed origin O , the points \(\mathrm { P } , \mathrm { Q }\) and R have coordinates \(( \mathbf { i } - 3 \mathbf { j } + \mathbf { k } ) , ( - 2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k } )\) and \(( 3 \mathbf { j } - 5 \mathbf { k } )\) respectively. The plane \(\Pi _ { 1 }\) passes through \(\mathrm { P } , \mathrm { Q }\) and R . Find
The plane \(\Pi _ { 2 }\) has equation \(\mathbf { r }\). ( \(\mathbf { i } + \mathbf { j } - \mathbf { k }\) ) \(= 6\). The planes \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\) intersect in the line I .
Find a vector equation of I, giving your answer in the form ( \(\mathbf { r } - \mathbf { a }\) ) \(\times \mathbf { b } = \mathbf { 0 }\).