Position vector from magnitude and bearing

Given the magnitude and direction (as a bearing or angle) of a position vector, express it in component form using i and j.

4 questions · Easy -1.1

1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors
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OCR MEI M1 2008 June Q2
6 marks Easy -1.2
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.
OCR H240/01 2019 June Q2
8 marks Moderate -0.8
2 The point \(A\) is such that the magnitude of \(\overrightarrow { O A }\) is 8 and the direction of \(\overrightarrow { O A }\) is \(240 ^ { \circ }\).
    1. Show the point \(A\) on the axes provided in the Printed Answer Booklet.
    2. Find the position vector of point \(A\). Give your answer in terms of \(\mathbf { i }\) and \(\mathbf { j }\). The point \(B\) has position vector \(6 \mathbf { i }\).
  2. Find the exact area of triangle \(A O B\). The point \(C\) is such that \(O A B C\) is a parallelogram.
  3. Find the position vector of \(C\). Give your answer in terms of \(\mathbf { i }\) and \(\mathbf { j }\).
OCR MEI M1 Q5
6 marks Moderate -0.8
5 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.
AQA Paper 2 2021 June Q12
1 marks Easy -1.8
12 A particle has a speed of \(6 \mathrm {~ms} ^ { - 1 }\) in a direction relative to unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{b7df05bf-f3fc-4705-a13c-6b562896fa9f-18_307_542_1528_749} The velocity of this particle can be expressed as a vector \(\left[ \begin{array} { l } v _ { 1 } \\ v _ { 2 } \end{array} \right] \mathrm { ms } ^ { - 1 }\) Find the correct expression for \(v _ { 2 }\) Circle your answer.
[0pt] [1 mark] \(v _ { 2 } = 6 \cos 30 ^ { \circ }\) \(v _ { 2 } = 6 \sin 30 ^ { \circ }\) \(v _ { 2 } = - 6 \sin 30 ^ { \circ }\) \(v _ { 2 } = - 6 \cos 30 ^ { \circ }\)