4MA0 Higher June 2017 Paper 4R Q21

EdexcelHigherOld spec5 marksVectors

21

Triangle OAB with X the midpoint of OA, W the midpoint of OB, and Y on AW

Diagram NOT accurately drawn

\(OAB\) is a triangle.

\(X\) is the midpoint of \(OA\) and \(W\) is the midpoint of \(OB\).

\(Y\) is the point on \(AW\) such that \(AY : YW = 2 : 1\)

\(\overrightarrow{OX} = 3\mathbf{a}\) and \(\overrightarrow{OW} = 3\mathbf{b}\)

(a) Express in terms of \(\mathbf{a}\) and \(\mathbf{b}\)
(i) \(\overrightarrow{AW}\)
(ii) \(\overrightarrow{AY}\)
(iii) \(\overrightarrow{XB}\) (3)
(b) Show by a vector method that \(XYB\) is a straight line. (2)
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