Review question

# Can we find the position vector of the intersection from the given ratios? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6007

## Question

The position vectors of three points $O, A$ and $B$ are $\begin{pmatrix}0\\0\end{pmatrix}, \begin{pmatrix}3\\3.5\end{pmatrix}$ and $\begin{pmatrix}6\\-1.5\end{pmatrix}$ respectively. Given that $\mathbf{OD} = \dfrac{1}{3}\mathbf{OB}$ and $\mathbf{AE} = \dfrac{1}{4}\mathbf{AB}$ write down the position vectors of $D$ and $E$.

Given also that $OE$ and $AD$ intersect at $X$, and that $\mathbf{OX} = p\:\mathbf{OE}$, and that $\mathbf{XD} = q\:\mathbf{AD}$, find the position vector of $X$ in terms of (i) $p$ (ii) $q$.

Hence calculate $p$ and $q$.