OCR MEI C4 2012 January — Question 7 5 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2012
SessionJanuary
Marks5
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Mark schemeDownload PDF ↗
TopicVectors 3D & Lines
TypeShow lines intersect and find intersection point
DifficultyModerate -0.3 This is a standard C4 vectors question requiring students to equate components and solve simultaneous equations to find where two lines meet. While it involves multiple steps (setting up three equations, solving for parameters, verifying the solution), the technique is routine and commonly practiced in textbooks, making it slightly easier than average for A-level.
Spec4.04e Line intersections: parallel, skew, or intersecting4.04f Line-plane intersection: find point
Show that the straight lines with equations \(\mathbf{r} = \begin{pmatrix} 4 \\ 2 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} 3 \\ 0 \\ 1 \end{pmatrix}\) and \(\mathbf{r} = \begin{pmatrix} -1 \\ 4 \\ 9 \end{pmatrix} + \mu \begin{pmatrix} -1 \\ 1 \\ 3 \end{pmatrix}\) meet. Find their point of intersection. [5] 
Show that the straight lines with equations $\mathbf{r} = \begin{pmatrix} 4 \\ 2 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} 3 \\ 0 \\ 1 \end{pmatrix}$ and $\mathbf{r} = \begin{pmatrix} -1 \\ 4 \\ 9 \end{pmatrix} + \mu \begin{pmatrix} -1 \\ 1 \\ 3 \end{pmatrix}$ meet.

Find their point of intersection. [5]

\hfill \mbox{\textit{OCR MEI C4 2012 Q7 [5]}}
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Q1 5 Q2 4 Q3 7 Q4 4 Q5 5 Q6 6 Q7 5 Q8 18 Q9 18