OCR MEI M1 2008 June — Question 2 6 marks

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2008
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors Introduction & 2D
TypePosition vector from magnitude and bearing
DifficultyEasy -1.2 This is a straightforward mechanics question testing basic vector concepts: sketching a 2D vector, calculating magnitude using Pythagoras, finding bearing from components using trigonometry, and scalar multiplication. All steps are routine applications of standard formulas with no problem-solving or insight required, making it easier than average.
Spec1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors

2 A particle has a position vector \(\mathbf { r }\), where \(\mathbf { r } = 4 \mathbf { i } - 5 \mathbf { j }\) and \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors in the directions east and north respectively.
  1. Sketch \(\mathbf { r }\) on a diagram showing \(\mathbf { i }\) and \(\mathbf { j }\) and the origin O .
  2. Calculate the magnitude of \(\mathbf { r }\) and its direction as a bearing.
  3. Write down the vector that has the same direction as \(\mathbf { r }\) and three times its magnitude.

2 A particle has a position vector $\mathbf { r }$, where $\mathbf { r } = 4 \mathbf { i } - 5 \mathbf { j }$ and $\mathbf { i }$ and $\mathbf { j }$ are unit vectors in the directions east and north respectively.\\
(i) Sketch $\mathbf { r }$ on a diagram showing $\mathbf { i }$ and $\mathbf { j }$ and the origin O .\\
(ii) Calculate the magnitude of $\mathbf { r }$ and its direction as a bearing.\\
(iii) Write down the vector that has the same direction as $\mathbf { r }$ and three times its magnitude.

\hfill \mbox{\textit{OCR MEI M1 2008 Q2 [6]}}