In maths we are currently doing vectors, and whilst I understand the basics I have no idea as of how to find the answer (all answers must be expressed in terms of x and y) to the current question (b and c)
I can do a quite easily, you just find a path from A to B which is part of a vector; so the answer is $-x+y$ (or $y-x$).
However to find AM (question b) neither of the given vectors have the same gradient so I cant't figure out at all how to get there. I thought the answer might have something to do with finding an "average" between the two vectors (maybe $-x+2/3(x+y)$ or something) to get to the middle but I am not sure.
What am I missing (apologies if the answer is very obvious!)?
Going from $A$ to $M$ is the same as going one third of the way from $A$ to $B$. In symbols:
$$\vec{AM} = \frac{1}{3}\vec{AB}$$
You already know what $\vec{AB}$ is, and so you now know what $\vec{AM}$ is:
\begin{eqnarray*} \vec{AM} &=& \frac{1}{3}\vec{AB} \\ \\ \\ &=& \frac{1}{3}({\bf y}-{\bf x}) \\ \\ \\ &=& \frac{1}{3}{\bf y} - \frac{1}{3}{\bf x} \end{eqnarray*}
To find $\vec{OM}$ you need to go from $O$ to $A$ to $M$:
$$\vec{OM} = \vec{OA} + \vec{AM}$$
Can you do this yourself?