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2 marksPosition Vectors

CSEC Mathematics · May/June 2012 · Paper 2 · Question 11(a)(iii)

The points A, B and C have position vectors OA = (6, 2), OB = (3, 4) and OC = (12, -2) respectively.

Draw a sketch to show the relative positions of A, B and C.

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Other parts of this question

  1. 11(a)(i)a)Express in the form (x, y) the vector BA.[2 marks]
  2. 11(a)(i)b)Express in the form (x, y) the vector BC.[2 marks]
  3. 11(a)(ii)State ONE geometrical relationship between BA and BC.[1 mark]
  4. 11(b)(i)Calculate the values of a and b such that (a-4, b) * (2, -4; 1, -3) = (20, 0; 0, 2).[3 marks]
  5. 11(b)(ii)Hence, or otherwise, write down the inverse of (2, -4; 1, -3).[2 marks]
  6. 11(b)(iii)Use the inverse of (2, -4; 1, -3) to solve for x and y in the matrix equation (2, -4; 1, -3) * (x, y) = (12, 7).[3 marks]

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