10 The line \(l\) has equation \(\mathbf { r } = 4 \mathbf { i } - 9 \mathbf { j } + 9 \mathbf { k } + \lambda ( - 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k } )\). The point \(A\) has position vector \(3 \mathbf { i } + 8 \mathbf { j } + 5 \mathbf { k }\).
- Show that the length of the perpendicular from \(A\) to \(l\) is 15 .
- The line \(l\) lies in the plane with equation \(a x + b y - 3 z + 1 = 0\), where \(a\) and \(b\) are constants. Find the values of \(a\) and \(b\).