Question

A regular hexagon, ABCDEF, has centre O.
→ →
OA = a and OB = b.
(a) Express, as simply as possible, in terms of a and/or b,
→
(i) DO,
→
(ii) AB,
→
(iii) DB.
(b) Explain why | a | = | b | = | b – a | .
(c) The points X, Y and Z are such that
→ → →
OX = a + b, OY = a – 2b and OZ = b – 2a.
(i) Express, as simply as possible, in terms of a and/or b,
→
(a) AX,
→
(b) YX. [1]
(ii) What can be deduced about Y, A and X?
→
(d) Express, as simply as possible, in terms of a and/or b, the vector XZ.
(e) Show that triangle XYZ is equilateral.
Area of triangle OAB