Vectors question: ABCDEF is a regular hexagon with centre O. M is the midpoint of BC. X is on AB extended, such that....

[shuphie]

MY WORKING:

Why I'm confused:
I realise that there is an easier alternative method to find EM and EX which are used in the mark scheme (purple), however I still want to understand why my method didn't work
1) When finding EM in my own working, why did i get 1/2 a + 2b instead of -1/2 a + 2b (which would factorise to 4b-a)? Where did I go wrong?
2) Why doesn't MX from my working have a shared factor of (4b-a) like EM and EX? Where did I go wrong?

Thank you

 

[Dr.Peterson]

I entirely missed this when posted. That sometimes happens when your posts are still being moderated (which they will not be now).

Here is your error:

​

The reality is that MX = MB + BX = 1/2 CB + BX = 1/2 a + 2/3 (b - a).

​

So watch your directions (and therefore signs) carefully!

(I didn't check all the rest after seeing this, so there may be other errors.)