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2 marksSimplifying Vector Expressions

CSEC Mathematics · 2003 (Specimen) · Paper 2 · Question 13(a)(i)

Vectors \vec{AB} = \begin{pmatrix} -1 \\ 2 \end{pmatrix} and \vec{BC} = \begin{pmatrix} 5 \\ 1 \end{pmatrix}.

Determine \vec{AC}.

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Other parts of this question

  1. 13(a)(ii)Calculate the magnitude of \vec{AC}.[2 marks]
  2. 13(a)(iii)Write the unit vector that is in the same direction as \vec{AC}.[1 mark]
  3. 13(b)(i) a)Express \vec{OR} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.[1 mark]
  4. 13(b)(i) b)Express \vec{OS} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.[1 mark]
  5. 13(b)(i) c)Express \vec{QP} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.[1 mark]
  6. 13(b)(i) d)Express \vec{SR} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.[2 marks]
  7. 13(b)(i) e)Express \vec{OT} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.[2 marks]
  8. 13(b)(i) f)Express \vec{ST} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.[1 mark]
  9. 13(b)(ii)Use the results of (d) and (f) above to prove that S, R and T lie in a straight line.[2 marks]

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