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3 marksVectors

CAPE Pure Mathematics Unit 1 · May/June 2001 · Paper 2 · Question 4(b)(ii)

The position vectors of points A and B relative to the origin, O, are 4i + j and i + 7j respectively. The point, C, lies on AB such that AC: CB = 2 : 1.

Find the position vector of C relative to O.

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Other parts of this question

  1. 4(a)Express the complex number, (z-1)/(z+1), in a similar form.[7 marks]
  2. 4(a)(i)Find the equation connecting x and y.[3 marks]
  3. 4(a)(ii)Show that the equation represents a circle, C.[3 marks]
  4. 4(a)(iii)Determine the centre and radius of C.[2 marks]
  5. 4(b)(i)Find the values of t such that the vector t r₁ + r₂ is perpendicular to the vector r₂ + r₃.[5 marks]
  6. 4(b)(iii)Determine cos AÔC.[2 marks]

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