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5 marksVectors

CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 2 · Question 3(b)(i)a)

The points P and Q have position vectors relative to the origin O given respectively by p = -i + 6j and q = 3i + 8j.

Calculate, in degrees, the size of the acute angle θ between p and q.

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Other parts of this question

  1. 3(a)(i)State the radius and the coordinates of the centre of C.[2 marks]
  2. 3(a)(ii)Find the equation of the tangent at the point (6, 8) on C.[4 marks]
  3. 3(a)(iii)Calculate the coordinates of the points of intersection of C with the straight line y = 2x + 3.[7 marks]
  4. 3(b)(i)b)Hence, calculate the area of triangle POQ.[2 marks]
  5. 3(b)(ii)a)Find, in terms of i and j, the position vector of M, where M is the midpoint of PQ.[2 marks]
  6. 3(b)(ii)b)Find, in terms of i and j, the position vector of R, where R is such that PQRO, labelled clockwise, forms a parallelogram.[3 marks]

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