GCSE vectors

(i cant read it fully but i am going with what i can understand)

the first part is to go from A to B.
but you dont know how to get straight from A to B, therefore you need to use a route you know, think of it like you are driving a car, but have no map. you can only use the routes which you already know.
the routes you know are a and b. so to get from A to B, you go A->O->B, then you put in the vectors. because you are going A to O, you are going in the opposite direction of a, so it is -a + b, (+b is the vector of O to B).
-a+b is written as b-a, as it looks better.

Thank you so much!

Do you mind helping me with the second bit? It says 'show that OC is parallel to BM'. Thank you!

Posted from TSR Mobile

OC will be parallel to BM if you can show that OC = k(BM) for some constant k.

So try working out expressions for vectors OC and BM in terms of vectors a and b.

Thank you very much!
OC will be a+b
but I'm not sure about BM. I can go to C (a) and I can go to D (b) but I'm not sure how to get to M from those points.

Well, you're told that M is the midpoint of CD so CM = MD. Also note that you're using equilateral triangles, so CD should be parallel (in fact equal) to another vector you have worked out already

Ah, I'm hopeless! I completely forgot that the answer to a) could be used!
So,
BM=b-1/2(b-a)
BM=b-1/2b+1/2a
2BM=2b-b+a
2BM=b+a
BM=1/2(a+b)
So this shows that BM is parallel to OC. Have I got it right?

Well, you're told that M is the midpoint of CD so CM = MD. Also note that you're using equilateral triangles, so CD should be parallel (in fact equal) to another vector you have worked out already

Yep, I would specifically state that since their direction vectors are multiples of each other, they have the same direction and are therefore parallel, but you're right so far.

Posted from TSR Mobile

A better term would be that they are scalar multiples therefore are parallel

Posted from TSR Mobile