Question

OABCDE is a regular hexagon. The points A and B have position vectors a and b respectively, referred to the origin O. Find, in terms of a and b the position vectors of C, D and E.

Answer 1

Given : \(\overline{OA} = \overline{a}, \overline{OB} = \overline{a}\) Let AD, BE, OC meet at M.

Then M bisects AD, BE, OC.

∵ OABM is a parallelogram

Hence, the position vectors of C, D and E are

respectively.