| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core (Further Pure Core) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Cross Product & Distances |
| Type | Angle between vectors using scalar product |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question testing standard cross product calculation and the relationship |u×v| = |u||v|sinθ. Part (a) requires computing a cross product and equating components (routine algebra), while part (b) applies a standard formula. The question is slightly above average difficulty due to being Further Maths content, but it's a textbook application with no novel insight required. |
| Spec | 4.04c Scalar product: calculate and use for angles4.04g Vector product: a x b perpendicular vector |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (a) | 1 |
| Answer | Marks |
|---|---|
| a = −3, b = −4 | B1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | oe |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (b) | u v |
| Answer | Marks |
|---|---|
| = 32.51… | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | s i n u v = u v must be used with their 𝐮 and 𝐯 |
Question 5:
5 | (a) | 1
u v = 2 + 2 a
− a
2 + 2a = b, −a = 3
a = −3, b = −4 | B1
M1
A1
[3] | 1.1
1.1
1.1 | oe
soi by correct equations
Both equations ft their 𝐮×𝐯
www
5 | (b) | u v
s in =
u v
26
=
9 10
= 32.51… | M1
A1FT
A1
[3] | 3.1a
1.1
1.1 | s i n u v = u v must be used with their 𝐮 and 𝐯
soi by correct expression for their sin𝜃. Formula alone is
M0.
ft their a and b, need not be simplified
33 or 0.57 rad or better5
\begin{enumerate}[label=(\alph*)]
\item Given that $\mathbf { u } = \left( \begin{array} { r } - 2 \\ 1 \\ 2 \end{array} \right) , \mathbf { v } = \left( \begin{array} { l } a \\ 0 \\ 1 \end{array} \right)$ and $\mathbf { u } \times \mathbf { v } = \left( \begin{array} { l } 1 \\ b \\ 3 \end{array} \right)$, find $a$ and $b$.
\item Using $\mathbf { u } \times \mathbf { v }$, determine the angle between the vectors $\mathbf { u }$ and $\mathbf { v }$, given that this angle is acute.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core 2024 Q5 [6]}}