Relative to origin $O$, the position vectors of points $A$, $B$ and $C$ are $\overrightarrow{OA} = \begin{pmatrix} 1 \\ -3 \\ 2 \end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix} -1 \\ 3 \\ 5 \end{pmatrix}$ and $\overrightarrow{OC} = \begin{pmatrix} 3 \\ 1 \\ -2 \end{pmatrix}$.
(i)[1]
Find the vector $\overrightarrow{AC}$.
(ii)[3]
The point $M$ is the midpoint of $AC$. Determine the unit vector that points in the direction of $\overrightarrow{OM}$.
(iii)[4]
Calculate $\overrightarrow{AB} \cdot \overrightarrow{AC}$ and so determine angle $BAC$.
(c(iii))[4]
Calculate $\overrightarrow{AB} \cdot \overrightarrow{AC}$ and so determine angle $BAC$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Gives $\vec{AC}=(2,4,-4)$.” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI