2 The points $A , B , C$ have position vectors

$$4 \mathbf { i } - 4 \mathbf { j } + \mathbf { k } , \quad - 4 \mathbf { i } + 3 \mathbf { j } - 4 \mathbf { k } , \quad 4 \mathbf { i } - \mathbf { j } - 2 \mathbf { k } ,$$

respectively, relative to the origin $O$.\\
(a) Find the equation of the plane $A B C$, giving your answer in the form $a x + b y + c z = d$.\\

(b) Find the perpendicular distance from $O$ to the plane $A B C$.\\

(c) The point $D$ has position vector $2 \mathbf { i } + 3 \mathbf { j } - 3 \mathbf { k }$.

Find the coordinates of the point of intersection of the line $O D$ with the plane $A B C$.\\

\hfill \mbox{\textit{CAIE Further Paper 1 2022 Q2}}