Review question

# Where do $ST$ and $AB$ cross? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8456

## Question

1. Given that $\overrightarrow{OM}=\mathbf{i}+3\mathbf{j}$ and $\overrightarrow{ON}=\mathbf{i}+\mathbf{j}$, evaluate $\overrightarrow{OM}.\overrightarrow{ON}$ and hence calculate $\widehat{MON}$ to the nearest degree.

2. The position vectors, relative to an Origin $O$, of two points $S$ and $T$ are $2\mathbf{p}$ and $2\mathbf{q}$ respectively. The point $A$ lies on $OS$ and is such that $OA=AS$. The point $B$ lies on $OT$ produced and is such that $OT=2TB$. The lines $ST$ and $AB$ intersect at $R$.

Given that $\overrightarrow{AR}=\lambda \overrightarrow{AB}$ and that $\overrightarrow{SR}=\mu \overrightarrow{ST}$, express $\overrightarrow{OR}$

1. in terms of $\mathbf{p}$, $\mathbf{q}$ and $\lambda$, (ii) in terms of $\mathbf{p}$, $\mathbf{q}$ and $\mu$.

Hence evaluate $\lambda$ and $\mu$ and express $\overrightarrow{OR}$ in terms of $\mathbf{p}$ and $\mathbf{q}$.