Review question

# If $A$, $P$ and $B$ are collinear, what's the value of $\lambda$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7285

## Question

Points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively relative to a point $O$. Given that $L$ is the midpoint of $OA$, and that $M$ is the point on $OB$ produced such that $OM = 3OB$, express $\overrightarrow{LM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.

Given further that $P$ is the point on $LM$ such that $LP = \lambda LM$, express $\overrightarrow{AP}$ in terms of $\mathbf{a, b}$ and $\lambda$.

In the case where $A, P$ and $B$ are collinear, calculate the value of

1. $\lambda$
2. $\dfrac{AP}{PB}$.