9 The plane \(p\) has equation \(3 x + 2 y + 4 z = 13\). A second plane \(q\) is perpendicular to \(p\) and has equation \(a x + y + z = 4\), where \(a\) is a constant.
- Find the value of \(a\).
- The line with equation \(\mathbf { r } = \mathbf { j } - \mathbf { k } + \lambda ( \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } )\) meets the plane \(p\) at the point \(A\) and the plane \(q\) at the point \(B\). Find the length of \(A B\).