4400 Higher June 2008 Paper 4 Q21

EdexcelHigherOld spec4 marksVectors

21 \(PQRSTU\) is a regular hexagon, centre \(O\).
The hexagon is made from six equilateral triangles of side 2.5 cm.

\(\overrightarrow{TU} = \mathbf{a}\). \(\overrightarrow{UP} = \mathbf{b}\).

(a) Find, in terms of \(\mathbf{a}\) and/or \(\mathbf{b}\), the vectors

(i) \(\overrightarrow{TP}\) (1)

(ii) \(\overrightarrow{PO}\) (1)

(iii) \(\overrightarrow{UO}\) (1)

(b) Find the modulus (magnitude) of \(\overrightarrow{UR}\). (1)

Scheme	Marks
(i) Answer: \(\mathbf{a} + \mathbf{b}\) oe	B1
(ii) Answer: \(-\mathbf{a}\) oe	B1
(iii) Answer: \(\mathbf{b} - \mathbf{a}\) oe	B1
	(3)