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OpenStudy (anonymous):
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
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