(i)[6]
Find the equation of plane $ABC$, and give your answer in the form $ax + by + cz = d$.
(ii)[1]
Find the position vector for $D$.
(iii)[4]
Show that the perpendicular distance from $A$ to $OD$ is $\frac{1}{3} \sqrt{65}$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The diagram depicts three points $A$, $B$ and $C$, with position vectors relative to the origin $O$ given by $\vec{OA} = \begin{pmatrix}2 \\ -1 \\ 2\end{pmatrix}$, $\vec{OB} = \begin{pmatrix}0 \\ 3 \\ 1\end{pmatrix}$ and $\vec{OC} = \begin{pmatrix}3 \\ 0 \\ 4\end{pmatrix}$. Point $D$ is situated on $BC$, between $B$ and $C$, and satisfies $CD = 2DB$.