11 The line \(l\) has equation \(\mathbf { r } = \mathbf { i } - 2 \mathbf { j } - 3 \mathbf { k } + \lambda ( - \mathbf { i } + \mathbf { j } + 2 \mathbf { k } )\). The points \(A\) and \(B\) have position vectors \(- 2 \mathbf { i } + 2 \mathbf { j } - \mathbf { k }\) and \(3 \mathbf { i } - \mathbf { j } + \mathbf { k }\) respectively.
- Find a unit vector in the direction of \(l\).
The line \(m\) passes through the points \(A\) and \(B\). - Find a vector equation for \(m\).
- Determine whether lines \(l\) and \(m\) are parallel, intersect or are skew.
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