Let O be the origin, vec{OP} = vec{a} and vec | vedclass

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(B) Given that $O$ is the origin, $\vec{OP} = \vec{a}$ and $\vec{OQ} = \vec{b}$.Since $R$ lies on $\vec{OP}$ such that $\vec{OP} = 5\vec{OR}$, we have

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$\frac{1}{5}(\vec{b}-4\vec{a})$

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(B) Given that $O$ is the origin, $\vec{OP} = \vec{a}$ and $\vec{OQ} = \vec{b}$.Since $R$ lies on $\vec{OP}$ such that $\vec{OP} = 5\vec{OR}$, we have $\vec{OR} = \frac{1}{5}\vec{OP} = \frac{1}{5}\vec{a}$.Given $\vec{OQ} = 5\vec{RM}$, we have $\vec{RM} = \frac{1}{5}\vec{OQ} = \frac{1}{5}\vec{b}$.Since $\vec{RM} = \vec{OM} - \vec{OR}$, we can write $\vec{OM} = \vec{RM} + \vec{OR} = \frac{1}{5}\vec{b} + \frac{1}{5}\vec{a}$.Now, $\vec{PM} = \vec{OM} - \vec{OP} = (\frac{1}{5}\vec{a} + \frac{1}{5}\vec{b}) - \vec{a} = \frac{1}{5}\vec{b} + \frac{1}{5}\vec{a} - \frac{5}{5}\vec{a} = \frac{1}{5}(\vec{b} - 4\vec{a})$.

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

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