4MA0 Higher January 2012 Paper 4 Q22

EdexcelHigherOld spec5 marksVectors

22

Rectangle OPQR with D on OP, E on OQ and F on PQ extended; OD = a and OR = 3b

Diagram NOT accurately drawn

\(OPQR\) is a rectangle.
\(D\) is the point on \(OP\) such that \(OD = \dfrac{1}{3}OP\).
\(E\) is the point on \(OQ\) such that \(OE = \dfrac{2}{3}OQ\).
\(PQF\) is the straight line such that \(QF = \dfrac{1}{3}PQ\).

\(\overrightarrow{OD} = \mathbf{a}\)    \(\overrightarrow{OR} = 3\mathbf{b}\)

(a) Find, in terms of \(\mathbf{a}\) and \(\mathbf{b}\),
(i) \(\overrightarrow{OQ}\)
(ii) \(\overrightarrow{OE}\)
(iii) \(\overrightarrow{DE}\)
(3)
(b) Use a vector method to prove that \(DEF\) is a straight line. (2)
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