What is the value of a.(b + c) in a Regular Hexagon?

[markyp23]

Homework Statement

"PRQSTU is a regular hexagon of side 2 units. PQ,QR and RS represent vectors a, b andc respectively. Find the value of a.(b + c)

The hexagon is a regular hexagon starting at the far left (ie pointing left) with P then anti clockwise through U at the top left.

Homework Equations

None that I can think of.

The Attempt at a Solution

I really don't know where to start. I've guessed that a (PQ) = -c. But I don't know where to go from there and now I'm really confused.

Any help greatly appreciated.

 

[Dick]

You must be drawing a pretty horrid picture of a hexagon to be guessing that a=(-c). If you draw a neat picture you will probably realize there is a special angular relationship between a and b+c. You could also just tough it out and compute the components of the vectors a, b and c, since you know their lengths and the angles between them.

 

[markyp23]

Thanks for the reply.

I think I realized why I was lost - it's because I was! We haven't been taught this part of vectors yet, and I was looking at a past paper.

Haha, oops. The picture was already printed for me and I thought that a=(-c). I better stick to diagrams of squares. :)