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3 marksVector Geometry Problems

CSEC Mathematics · May/June 2016 · Paper 2 · Question 11(a)(ii)

The position vectors of points A, B and C, relative to the origin O, are OA = (-2, 2), OB = (6, 1) and OC = (10, 4) respectively.

Hence, determine whether A, B and C are collinear, giving the reasons for your answer.

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Other parts of this question

  1. 11(a)(i)Express in the form (x, y) the vectors AB and AC.[3 marks]
  2. 11(b)Determine the value of x for which the matrix (3, x; 2, 4) is singular.[2 marks]
  3. 11(c)(i)Determine NP.[1 mark]
  4. 11(c)(ii)Given that PN = (19, 11; 11, 4), determine whether matrix multiplication is commutative.[1 mark]
  5. 11(c)(iii)Determine N^-1, the inverse of N.[2 marks]
  6. 11(c)(iv)Hence, calculate the values of x and y for which (4, 1; 3, 2) * (x, y) = (1, 2).[3 marks]

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