With origin $O$ as the reference point, the points $A$, $B$, $C$ and $D$ are described by the position vectors $\overrightarrow{OA} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix} 1 \\ 2 \\ -3 \end{pmatrix}$, $\overrightarrow{OC} = \begin{pmatrix} 1 \\ -2 \\ 5 \end{pmatrix}$ and $\overrightarrow{OD} = \begin{pmatrix} 5 \\ -6 \\ 11 \end{pmatrix}$.
(a)[3]
Determine the obtuse angle between the vectors $\overrightarrow{OA}$ and $\overrightarrow{OB}$.
(b)[2]
The line $l$ passes through the points $A$ and $B$. Derive a vector equation for the line $l$.
(c)[4]
Find the position vector of the point where line $l$ meets the line through $C$ and $D$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the correct procedure to evaluate the scalar product of $\vec{OA}$ and $\vec{OB}$.” …