Let O be the origin, OP= a and OQ= b.

Question

Let $O$ be the origin, $\vec{OP}=\vec a$ and $\vec{OQ}=\vec b$. Let $R$ be the point on $OP$ such that $OP=5\,OR$, and $M$ be the point such that $OQ=5\,RM$. Then $\vec{PM}$ is equal to:

Accepted Answer

$\vec{OR} = \dfrac{\vec{OP}}{5} = \dfrac{\vec a}{5}$, $\vec{RM} = \dfrac{\vec{OQ}}{5} = \dfrac{\vec b}{5}$.

$$\vec{OM} = \vec{OR}+\vec{RM} = \frac{\vec a+\vec b}{5}$$
$$\vec{PM} = \vec{OM}-\vec{OP} = \frac{\vec a+\vec b}{5}-\vec a = \frac{\vec b-4\vec a}{5}$$

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