Mathematics 0580 · IGCSE · Vector geometry

Vector geometry — practice question

$OPQR$ forms a rectangle, with $O$ at the origin. $M$ lies halfway along $RQ$, and $PT:TQ=2:1$. $\overrightarrow{OP}=\mathbf{p}$ and $\overrightarrow{OR}=\mathbf{r}$.
(a(i))[1]

Find, in terms of $\mathbf{p}$ and/or $\mathbf{r}$, the vector $\overrightarrow{MQ}$ in its simplest form.

(a(ii))[1]

Find the vector $\overrightarrow{MT}$.

(a(iii))[1]

Find the vector $\overrightarrow{OT}$.

(b)[2]

Find the position vector of $U$, expressed using $\mathbf{p}$ and $\mathbf{r}$. Give your answer in its simplest form.

(c)[3]

Find the positive value for $k$.

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