OCR H240/02 2018 September — Question 8 9 marks

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Year2018
SessionSeptember
Marks9
TopicVectors 3D & Lines
TypeLinear combinations of vectors
DifficultyModerate -0.5 This is a straightforward vector geometry question involving a cuboid with clearly defined structure. Finding the midpoint M requires basic vector addition (identifying U's position vector as a+b+c, then averaging with a), which is a standard textbook exercise requiring minimal problem-solving insight. The visual aid and structured setup make it easier than average.
Spec1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement

8 The points \(A , B\) and \(C\) have position vectors \(\mathbf { a } , \mathbf { b }\) and \(\mathbf { c }\), relative to an origin \(O\), in three dimensions. The figure \(O A P B S C T U\) is a cuboid, with vertices labelled as in the following diagram. \(M\) is the midpoint of \(A U\). \includegraphics[max width=\textwidth, alt={}, center]{85de9a39-f8be-40ee-b0c8-e2e632be93d8-5_557_1221_2087_420}

8 The points $A , B$ and $C$ have position vectors $\mathbf { a } , \mathbf { b }$ and $\mathbf { c }$, relative to an origin $O$, in three dimensions. The figure $O A P B S C T U$ is a cuboid, with vertices labelled as in the following diagram. $M$ is the midpoint of $A U$.\\
\includegraphics[max width=\textwidth, alt={}, center]{85de9a39-f8be-40ee-b0c8-e2e632be93d8-5_557_1221_2087_420}

\hfill \mbox{\textit{OCR H240/02 2018 Q8 [9]}}