OCR MEI Further Pure Core Specimen — Question 1 3 marks

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
SessionSpecimen
Marks3
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Mark schemeDownload PDF ↗
TopicVectors: Lines & Planes
TypeAngle between two lines
DifficultyModerate -0.5 This is a standard Further Maths vector geometry question requiring extraction of direction vectors and application of the scalar product formula cos θ = (a·b)/(|a||b|). While it involves multiple steps (dot product, magnitudes, inverse cosine), it's a routine textbook exercise with no conceptual challenges, making it slightly easier than average even for Further Maths.
Spec4.04a Line equations: 2D and 3D, cartesian and vector forms4.04c Scalar product: calculate and use for angles
Find the acute angle between the lines with vector equations \(\mathbf{r} = \begin{pmatrix} 3 \\ 0 \\ -2 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ 2 \\ -1 \end{pmatrix}\) and \(\mathbf{r} = \begin{pmatrix} 1 \\ 5 \\ 3 \end{pmatrix} + \mu \begin{pmatrix} 3 \\ 1 \\ -2 \end{pmatrix}\). [3]
Question 1:
AnswerMarks
1(cid:167) 1 (cid:183) (cid:167) 3 (cid:183)
(cid:168) (cid:184) (cid:168) (cid:184)
2 . 1 (cid:32)7
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:169)(cid:16)1(cid:185) (cid:169)(cid:16)2(cid:185)
7
cos(cid:84)(cid:32) (cid:32)0.7637...
6(cid:117) 14
AnswerMarks
(cid:84)(cid:32)40.2(cid:113) or 0.702 radiansM1
M1
A1
AnswerMarks
[3]1.1
1.1
AnswerMarks Guidance
1.1n
13 0
2i2 0
2ii3 0
3i2 0
3iiA2 0
3iiB0 1
3iiC1 0 
Question 1:
1 | (cid:167) 1 (cid:183) (cid:167) 3 (cid:183)
(cid:168) (cid:184) (cid:168) (cid:184)
2 . 1 (cid:32)7
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:169)(cid:16)1(cid:185) (cid:169)(cid:16)2(cid:185)
7
cos(cid:84)(cid:32) (cid:32)0.7637...
6(cid:117) 14
(cid:84)(cid:32)40.2(cid:113) or 0.702 radians | M1
M1
A1
[3] | 1.1
1.1
1.1 | n
1 | 3 | 0 | 0 | 0 | 3
2i | 2 | 0 | 0 | 0 | 2
2ii | 3 | 0 | 1 | 0 | 4
3i | 2 | 0 | 0 | 0 | 2
3iiA | 2 | 0 | 0 | 0 | 2
3iiB | 0 | 1 | 0 | 0 | 1
3iiC | 1 | 0 | 0 | 0 | 1
Find the acute angle between the lines with vector equations $\mathbf{r} = \begin{pmatrix} 3 \\ 0 \\ -2 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ 2 \\ -1 \end{pmatrix}$ and $\mathbf{r} = \begin{pmatrix} 1 \\ 5 \\ 3 \end{pmatrix} + \mu \begin{pmatrix} 3 \\ 1 \\ -2 \end{pmatrix}$. [3]

\hfill \mbox{\textit{OCR MEI Further Pure Core  Q1 [3]}}
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Q1 3 Q2 6 Q3 6 Q4 5 Q5 7 Q6 6 Q7 11 Q8 5 Q9 7 Q10 9 Q11 9 Q12 13 Q13 13 Q14 18 Q15 8 Q16 18