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3 marksVector Geometry Problems

CSEC Mathematics · January 2010 · Paper 2 · Question 13(b)(iii)

OE, EF, and MF are straight lines. H is such that EF = 3EH. G is such that MF = 5MG. M is the midpoint of OE. Vector OM = v and EH = u.

Hence, prove that O, G, and H lie on a straight line.

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Other parts of this question

  1. 13(a)(i)a)Express the vector OB in the form [a b].[3 marks]
  2. 13(a)(i)b)Express the vector OA + OB in the form [a b].[3 marks]
  3. 13(a)(ii)Determine the values of x and y.[2 marks]
  4. 13(b)(i)a)Write an expression for vector HF in terms of u and/or v.[1 mark]
  5. 13(b)(i)b)Write an expression for vector MF in terms of u and/or v.[2 marks]
  6. 13(b)(i)c)Write an expression for vector OH in terms of u and/or v.[2 marks]
  7. 13(b)(ii)Show that vector OG = (3/5)(2v + u).[2 marks]

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