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 $3 \mathbf { i } + 8 \mathbf { j } + 5 \mathbf { k }$.\\
(i) Show that the length of the perpendicular from $A$ to $l$ is 15 .\\
(ii) 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 $b$.

\hfill \mbox{\textit{CAIE P3 2014 Q10}}