The position vectors of P and Q are respectiv | vedclass

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Question

(A) Let $\overrightarrow{p} = \overrightarrow{a}$ and $\overrightarrow{q} = \overrightarrow{b}$ be the position vectors of points $P$ and $Q$ respecti

Vedclass · Accepted Answer

$5 \overrightarrow{b}-4 \overrightarrow{a}$

Vedclass · Answer

(A) Let $\overrightarrow{p} = \overrightarrow{a}$ and $\overrightarrow{q} = \overrightarrow{b}$ be the position vectors of points $P$ and $Q$ respectively.Given that $\overrightarrow{PR} = 5 \overrightarrow{PQ}$.We know that $\overrightarrow{PR} = \overrightarrow{r} - \overrightarrow{p}$ and $\overrightarrow{PQ} = \overrightarrow{q} - \overrightarrow{p}$.Substituting these into the given equation:$\overrightarrow{r} - \overrightarrow{p} = 5(\overrightarrow{q} - \overrightarrow{p})$$\overrightarrow{r} - \overrightarrow{a} = 5(\overrightarrow{b} - \overrightarrow{a})$$\overrightarrow{r} = \overrightarrow{a} + 5\overrightarrow{b} - 5\overrightarrow{a}$$\overrightarrow{r} = 5\overrightarrow{b} - 4\overrightarrow{a}$Thus,the position vector of $R$ is $5\overrightarrow{b} - 4\overrightarrow{a}$.

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$,then the position vector of $R$ is

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