Using the origin $O$ as the reference point, the position vectors of the points $A$, $B$ and $C$ are $
\overrightarrow{OA} = i + 2j + 3k$, $\overrightarrow{OB} = 2i + 4j + k$ and $\overrightarrow{OC} = 3i + 5j - 3k$.
(i)[4]
Determine the exact value of $\cos$ of angle $BAC$.
(ii)[3]
Hence determine the exact area of triangle $ABC$.
(iii)[5]
Find the equation of the plane parallel to the $y$-axis that contains the line through $B$ and $C$. Present your answer in the form $ax + by + cz = d$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Give or indicate $\overrightarrow{AB}$ and $\overrightarrow{AC}$ in component form” …