OCR MEI C4 2013 June — Question 4 8 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2013
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors 3D & Lines
TypeLine-plane intersection and related angle/perpendicularity
DifficultyModerate -0.3 This is a straightforward three-part question on 3D coordinate geometry covering standard techniques: finding a line equation from two points, finding line-plane intersection by substitution, and calculating an angle using dot product. All parts follow routine procedures with no conceptual challenges, making it slightly easier than average, though the multi-step nature and 8 total marks keep it from being trivial.
Spec4.04a Line equations: 2D and 3D, cartesian and vector forms4.04b Plane equations: cartesian and vector forms4.04c Scalar product: calculate and use for angles4.04f Line-plane intersection: find point

  1. Find a vector equation of the line \(l\) joining the points \((0, 1, 3)\) and \((-2, 2, 5)\). [2]
  2. Find the point of intersection of the line \(l\) with the plane \(x + 3y + 2z = 4\). [3]
  3. Find the acute angle between the line \(l\) and the normal to the plane. [3]

Question 4:
4
Question 4:
4
\begin{enumerate}[label=(\roman*)]
\item Find a vector equation of the line $l$ joining the points $(0, 1, 3)$ and $(-2, 2, 5)$. [2]

\item Find the point of intersection of the line $l$ with the plane $x + 3y + 2z = 4$. [3]

\item Find the acute angle between the line $l$ and the normal to the plane. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C4 2013 Q4 [8]}}