A-level · Vectors

Modelling with vectorsExam-style questions

Vectors as physical quantities — displacement, velocity and force — with constant-velocity motion r = r₀ + tv, speed as the magnitude of velocity, bearings from north, resultant forces and equilibrium, and "passes through O".

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3 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

  1. 1
    A particle moves with constant velocity (2i−j+2k)(2\mathbf{i} - \mathbf{j} + 2\mathbf{k}) m s−1^{-1} and starts at the point (i+2j−k)(\mathbf{i} + 2\mathbf{j} - \mathbf{k}) m. Find its speed and its position vector after 33 seconds.
    Level 3 · 3 marksTry it
  2. 2
    A particle moves so that its position vector at time tt seconds is r=(3i+2j)+t(4i−j)\mathbf{r} = (3\mathbf{i} + 2\mathbf{j}) + t(4\mathbf{i} - \mathbf{j}) metres.
    (a) Find the position of the particle when t=2t = 2. (2 marks)
    (b) Find the speed of the particle, to 3 s.f. (3 marks)
    (c) Find the distance of the particle from the origin when t=2t = 2. (2 marks)
    Level 3 · 7 marksTry it
  3. 3
    Two particles AA and BB move with position vectors rA=(i+2j)+t(2i+j)\mathbf{r}_A = (\mathbf{i} + 2\mathbf{j}) + t(2\mathbf{i} + \mathbf{j}) and rB=7i+t(−i+2j)\mathbf{r}_B = 7\mathbf{i} + t(-\mathbf{i} + 2\mathbf{j}) at time tt seconds.
    (a) Show that the particles collide, and find the time of collision. (4 marks)
    (b) Find the position vector at which they collide. (2 marks)
    Level 3 · 6 marksTry it