Question

Let ABCDEF be a regular hexagon. If

Answer 1

Let ABCDEF be a regular hexagon. If􀀀!AB = a and
􀀀􀀀!BC = b, express each of the following as linear combinations of a and b:
(a)􀀀􀀀!CD; (b)􀀀􀀀!DA; (c)􀀀􀀀!EB.

Answer 2

ab, bc are vectors

Answer 3

I can't read your notation there. But I'm sure you already know that all the vectors have to be the same length, and the angles are determined by the vertex angles of a hexagon.

Answer 4

yep

Answer 5

hmm, actually depending on how you label your vertices, AD and BE are diagonals, not sides and will have different lengths.

Answer 6

Probably best to start by drawing a regular hexagon and overlaying a coordinate grid with origin at a convenient vertex.

Answer 7

I'd probably do something like this:

I think that would be easier to get the vector components of everything you need.

Answer 8

A little basic geometry will get all the lengths and coordinates of vertices you need.

Answer 9

in the terms of a and b?

Answer 10

Sure. First start from that picture and get a and b in xi +yj vector component form, then once you know the distances and angles between any two vertices, you can convert that information into vectors.

Answer 11

ok, thanks

Answer 12

You're welcome. This is a fun one. I'm going to try to work it out. If you get an answer or something good along the way, let me know so I can check my own work.

Answer 13

ok, sounds good