Question

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

• A. $5\overline{b}-4\overline{a}$
• B. $5\overline{b}+4\overline{a}$
• C. $4\overline{b}-5\overline{a}$
• D. $4\overline{b}+5\overline{a}$

Answer 1

The correct option is A $5\overline{b}-4\overline{a}$

$\overrightarrow{OP}=\overline{a}$

$\overrightarrow{OQ}=\overrightarrow{b}$

$\overrightarrow{PQ}=\overrightarrow{b}-\overrightarrow{a}$

$\overline{PR}=5\overline{PQ}$

to find $\overrightarrow{OR}$

$\overrightarrow{PR}=\overrightarrow{OR}-\overrightarrow{OP}$

$5\overrightarrow{PQ}=\overrightarrow{OR}-\overrightarrow{OP}$

Now putting values

$5(\overrightarrow{b}-\overrightarrow{a})=\overrightarrow{OR}-\overrightarrow{a}$

$\overrightarrow{OR}=5\overrightarrow{b}-5\overrightarrow{b}+\overrightarrow{a}$

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