10 The line \(l\) has equation \(\mathbf { r } = 5 \mathbf { i } - 3 \mathbf { j } - \mathbf { k } + \lambda ( \mathbf { i } - 2 \mathbf { j } + \mathbf { k } )\). The plane \(p\) has equation $$( \mathbf { r } - \mathbf { i } - 2 \mathbf { j } ) \cdot ( 3 \mathbf { i } + \mathbf { j } + \mathbf { k } ) = 0$$ The line \(l\) intersects the plane \(p\) at the point \(A\).

1. Find the position vector of \(A\).
2. Calculate the acute angle between \(l\) and \(p\).
3. Find the equation of the line which lies in \(p\) and intersects \(l\) at right angles.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.