With regard to the origin $O$, the position vectors for the points $A$ and $B$ are $vec{OA} = \begin{pmatrix}1\\2\\-1\end{pmatrix}$ and $\vec{OB} = \begin{pmatrix}0\\3\\1\end{pmatrix}$.
(a)[3]
Find a vector equation of the line $l$ that passes through $A$ and $B$.
(b)[2]
Point $C$ is on $l$ and satisfies $\vec{AC} = 3\vec{AB}$. Find the position vector of $C$.
(c)[5]
Find the possible position vectors of the point $P$ on $l$ for which $OP = \sqrt{14}$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain direction vector $-\mathbf{i}+\mathbf{j}+2\mathbf{k}$” …