Review question

If $C$ is on this line, can we find the ratio $AC:CB$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5153

Question

Relative to an origin $O$, the position vectors of two points, $A$ and $B$, are $\begin{pmatrix}2\\5\end{pmatrix}$ and $\begin{pmatrix}4\\1\end{pmatrix}$ respectively. The point $C$ is on $AB$. Given that the position of $C$ is $\begin{pmatrix}2t\\t\end{pmatrix}$, find the ratio $AC:CB$.

The point $D$ is on $OC$, between $O$ and $C$, and $\widehat{ADB}$ is a right angle. Given that the position vector of $D$ is $\begin{pmatrix}2s\\s\end{pmatrix}$, find the value of $s$.