(i)[6]
Determine the equation of the plane $ABC$, and express it in the form $ax + by + cz = d$.
(ii)[1]
Determine the position vector of $D$.
(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 $C$ whose position vectors relative to the origin $O$ are $\vec{OA} = \begin{pmatrix}2\\-1\\2\end{pmatrix}$, $\vec{OB} = \begin{pmatrix}0\\3\\1\end{pmatrix}$ and $\vec{OC} = \begin{pmatrix}3\\0\\4\end{pmatrix}$. The point $D$ lies on $BC$, with $B$ and $C$ as the end points, and satisfies $CD = 2DB$.