Vector $a=(\begin{matrix}2\\1\end{matrix})$ , vector $b=(\begin{matrix}-2\\1\end{matrix})$.

On each grid below, draw a vector to represent

Given that

      $m(\begin{matrix}4\\1\end{matrix})+n(\begin{matrix}5\\2\end{matrix})=(\begin{matrix}12\\6\end{matrix})$

find the value of $m$ and the value of $n$.

$m$ = .......................

$n$ = .......................

P, Q, R and S are the midpoints of OX, XY, YZ and OZ respectively.

$\overset{\rightarrow}{OP}=a$ , $\overset{\rightarrow}{XQ}=b$ and $\overset{\rightarrow}{OS}=c$.

Show that $PQ$ is parallel to $SR$.

Two vectors, a and b, are shown on the 1 centimetre grid below.

Show that the vector a + 2b has length 7cm.
You may use the grid below.