8 The points \(A , B\) and \(C\) have position vectors \(\overrightarrow { \mathrm { OA } } = - 2 \mathbf { i } + \mathbf { j } + 4 \mathbf { k } , \overrightarrow { \mathrm { OB } } = 5 \mathbf { i } + 2 \mathbf { j }\) and \(\overrightarrow { \mathrm { OC } } = 8 \mathbf { i } + 5 \mathbf { j } - 3 \mathbf { k }\), where \(O\) is the origin. The line \(l _ { 1 }\) passes through \(B\) and \(C\).

1. Find a vector equation for \(l _ { 1 }\).
   The line \(l _ { 2 }\) has equation \(\mathbf { r } = - 2 \mathbf { i } + \mathbf { j } + 4 \mathbf { k } + \mu ( 3 \mathbf { i } + \mathbf { j } - 2 \mathbf { k } )\).
2. Find the coordinates of the point of intersection of \(l _ { 1 }\) and \(l _ { 2 }\).
3. The point \(D\) on \(l _ { 2 }\) is such that \(\mathrm { AB } = \mathrm { BD }\). Find the position vector of \(D\).
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