Question

A regular hexagon is shown below. O is

the centre of the hexagon.
AB = 3p+q
BC = 4p
a) Write AO in terms of p and/or q.
b) Write OB in terms of p and/or q.
c) Write EB in terms of p and/or q.
Give each answer in its simplest form.
A
B
3p+q
4p
8
C
D

Answer 1

The expression of the vectors are:

Vector AO : 1.5p + 0.5q.

Vector OB: 2p.

Vector EB: 1.5p + 0.5q.

How to find the hexagon vectors?

We want to find vector AO, vector OB, and vector EB in terms of p and/or q.

Let's solve these one by one to get:

Vector AO: As O is the center of the hexagon, vector AO is half of AB. Thus:

Vector AO = 1/2 * AB

= ¹/₂ * (3p + q)

= 1.5p + 0.5q.

Vector OB: Similarly as above, OB is half of BC. Thus:

Vector OB = ¹/₂ * BC = 1/2 * 4p = 2p.

Vector EB: EB is the sum of EA and AB. Since EA is equal to -AO, we waill have:

Vector EB = -AO + AB

= -1.5p - 0.5q + 3p + q

= 1.5p + 0.5q.