4MA0 Higher January 2014 Paper 4R Q18

EdexcelHigherOld spec5 marksPythagoras Vectors

Diagram NOT accurately drawn

\(ABCDEF\) is a regular hexagon, centre \(O\).

\(\overrightarrow{AB} = \mathbf{p}\) and \(\overrightarrow{AF} = \mathbf{q}\)

(a) Express in terms of \(\mathbf{p}\) and \(\mathbf{q}\)

(i) \(\overrightarrow{AO}\)

(ii) \(\overrightarrow{AD}\)

(iii) \(\overrightarrow{AC}\)

(3)

(b) Given that \(\mathbf{p} = \begin{pmatrix} \sqrt{3} \\ 1 \end{pmatrix}\) centimetres,
find the length of a side of the hexagon. (2)

Scheme	Marks
(i) Answer: \(\mathbf{p} + \mathbf{q}\) oe	B1
(ii) Answer: \(2\mathbf{p} + 2\mathbf{q}\) oe	B1
(iii) Answer: \(2\mathbf{p} + \mathbf{q}\) oe	B1
	(3)