OCR MEI C4 2007 June — Question 2 4 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2007
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors: Lines & Planes
TypeParallel and perpendicular planes
DifficultyEasy -1.2 This is a straightforward recall question requiring students to identify normal vectors from plane equations (direct reading of coefficients) and verify perpendicularity using the dot product equals zero. It involves minimal steps, no problem-solving insight, and tests only basic vector operations that are routine exercises in C4.
Spec4.04b Plane equations: cartesian and vector forms4.04c Scalar product: calculate and use for angles

2 Write down normal vectors to the planes \(2 x + 3 y + 4 z = 10\) and \(x - 2 y + z = 5\).
Hence show that these planes are perpendicular to each other.

Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
Comparing with \(x = b\theta - a\sin\theta\), \(y = a - a\cos\theta\): here \(a = 0.25\), \(b = 7\)B1 Identifying parameters
Wavelength \(= 2\pi b = 14\pi \approx 44.0\) (units)B1
Height \(= 2a = 0.5\) (units)B1
# Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Comparing with $x = b\theta - a\sin\theta$, $y = a - a\cos\theta$: here $a = 0.25$, $b = 7$ | B1 | Identifying parameters |
| Wavelength $= 2\pi b = 14\pi \approx 44.0$ (units) | B1 | |
| Height $= 2a = 0.5$ (units) | B1 | |

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2 Write down normal vectors to the planes $2 x + 3 y + 4 z = 10$ and $x - 2 y + z = 5$.\\
Hence show that these planes are perpendicular to each other.

\hfill \mbox{\textit{OCR MEI C4 2007 Q2 [4]}}