In the diagram, X and Y are midpoints of AC and BC respectively.
$\overrightarrow{\mathrm{AC}}=\text{p}$ and $\overrightarrow{\mathrm{BC}}=\text{q}$. (a) In terms of p and/or q, find:
(i) $\overrightarrow{\mathrm{XA}}$,

(ii) $\overrightarrow{\mathrm{AB}}$.

(b) Show that $\overrightarrow{\mathrm{XY}}$ and $\overrightarrow{\mathrm{AB}}$ are parallel.

The diagram shows triangle APQ.
$\overrightarrow{\mathrm{AP}}=\text{p}$ and $\overrightarrow{\mathrm{AQ}}=\text{q}$ and $PB=\frac{1}{3}PQ$. Find $\overrightarrow{\mathrm{AB}}$ in terms of p and q, giving your answer in its simplest form.

The diagram shows DEFNM and its image ABCNM after a reflection along the line NM.
AB = BC = CN = AM and $C\hat{N}M=A\hat{M}N={90}^O$. Expressing your answer, in terms of a, b and/or c, in simplest form, find:
(a) $\overrightarrow{\mathrm{MC}}$,

(b) $\overrightarrow{\mathrm{MF}}$,

(c) $\overrightarrow{\mathrm{FB}}$.

In the diagram, $\overrightarrow{Q}R$ = $a$ and $\overrightarrow{S}T$ = $b$.
R is the point on QS such that $\overrightarrow{Q}S$ = $3\overrightarrow{Q}R$.
U is the point on RP such that $\overrightarrow{R}P$ = $4\overrightarrow{R}U$.
T is the midpoint of SP. (a) Express, as simply as possible, in terms of a and/or b:
(i) $\overrightarrow{R}S$,

(ii) $\overrightarrow{R}P$,

(iii) $\overrightarrow{U}Q$,

(iv) $\overrightarrow{T}Q$.

(b) Write down two facts about the points T, U and Q.

(a) The magnitude of $\overrightarrow{A}B$ is 10 units.
One of the entries of the vector is 8.
Point A is located North West of B.
Write $\overrightarrow{A}B$ as a column vector.

In the diagram, $\overrightarrow{O}A$ = $a$, $\overrightarrow{O}B$ = $b$, $\overrightarrow{B}X$ = $\frac{1}{4}\overrightarrow{B}A$ and $\overrightarrow{B}Y$ = $ka$. (a) Express, as simply as possible, in terms of a, b and/or k:
(i) $\overrightarrow{A}B$,

(ii) $\overrightarrow{O}Y$,

(iii) $\overrightarrow{O}X$.

(b) Given that OX is parallel to AY, find the value of k.

In the diagram, O is the origin, $\overrightarrow{O}A$ = $a$, $\overrightarrow{O}B$ = $b$, and ON : NB = 1 : 2.
M is the midpoint of AB. Express in terms of a and/or b, in its simplest form:
(a) $\overrightarrow{A}B$,

(b) The position vector of M,

(c) $\overrightarrow{M}N$.

In the diagram, $\overrightarrow{O}A$ = $a$, $\overrightarrow{O}B$ = $b$, $\overrightarrow{B}Q$ = $kb+a$ and $\overrightarrow{O}P$ = $\frac{2}{3}a+\frac{1}{3}b$. (a) Express $\overrightarrow{A}B$ in terms of a and/or b.

(b) $\overrightarrow{A}Q$ in terms of k, a and/or b.

(c) Find the ratio of AP to PB.

(d) Given that OP is parallel to BQ, find the value of k.

In the diagram, $\overrightarrow{O}R$ = $3b$, $\overrightarrow{O}P$ = $4a$ and $\overrightarrow{R}S$ = $6a$.
Q lies on PR such that PQ : QR = 2 : 3. (a) Find the following in terms of a and b, giving each answer in its simplest form.
(i) $\overrightarrow{P}R$,

(ii) $\overrightarrow{O}Q$.

(b) Find $\overrightarrow{O}S$, in terms of a and b and hence show that $\overrightarrow{O}Q$ = $\frac{2}{5}\overrightarrow{O}S$.