| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 5 |
| Topic | Vectors Introduction & 2D |
| Type | Geometric properties using vectors |
| Difficulty | Moderate -0.8 This is a straightforward vector question requiring only basic operations: finding a midpoint using the midpoint formula, calculating magnitude, and using vector equality to find a position vector. All steps are routine applications of standard formulas with no problem-solving insight needed. The 'show that' format makes it even more mechanical since students know the target answer. |
| Spec | 1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement |
The points A, B and C have position vectors $\mathbf{3i - 4j + 2k}$, $\mathbf{-i + 6k}$ and $\mathbf{7i - 4j - 2k}$ respectively.
M is the midpoint of BC.
\begin{enumerate}[label=(\alph*)]
\item Show that the magnitude of $\overrightarrow{OM}$ is equal to $\sqrt{17}$. [2]
\end{enumerate}
Point D is such that $\overrightarrow{BC} = \overrightarrow{AD}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show that position vector of the point D is $\mathbf{1i - 8j - 6k}$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2017 Q2 [5]}}