13.

(a)

In triangle ABC, not drawn to scale P and Q are the midpoints of AB and BC

respectively.

(i) Make a sketch of the diagram and show the points P and Q.

(ii) Given that \vec{AB}=2x and \vec{BC}=3y write, in terms of x and y an expression for

B

C

whad to determine

a) \vec{AC}

b) \overline{PO}

(iii) Hence show that \vec{PQ}=\frac{1}{2}\vec{AC}

(b) The position vectors of the points R, S and T relative to the origin are \overline{OR}=(\begin{matrix}3\\ 4\end{matrix}) \overline{OS}=(\begin{matrix}-1\\ 6\end{matrix}) \overline{OT}=(\begin{matrix}5\\ -2\end{matrix})

(i) Expres in the form \binom{a}{b} the vectors

a) \vec{RT}

b) \vec{SR}