OCR H240/01 2017 Specimen — Question 2 5 marks

Exam BoardOCR
ModuleH240/01 (Pure Mathematics)
Year2017
SessionSpecimen
Marks5
TopicVectors Introduction & 2D
TypeGeometric properties using vectors
DifficultyModerate -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.
Spec1.10d 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.
  1. Show that the magnitude of \(\overrightarrow{OM}\) is equal to \(\sqrt{17}\). [2]
Point D is such that \(\overrightarrow{BC} = \overrightarrow{AD}\).
  1. Show that position vector of the point D is \(\mathbf{1i - 8j - 6k}\). [3]

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]}}