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

• Correct answer
  A

  $5 \overrightarrow{\mathbf{b}}-4 \overrightarrow{\mathbf{a}}$
• B

  $5 \overrightarrow{\mathbf{b}}+4 \overrightarrow{\mathbf{a}}$
• C

  $4 \overrightarrow{\mathbf{b}}-5 \overrightarrow{\mathbf{a}}$
• D

  $4 \overrightarrow{\mathbf{b}}+5 \overrightarrow{\mathbf{a}}$

Solution

Given that,
It mean $R$ divides $P Q$ externally in the ratio $5: 4$. $$ \begin{aligned} \therefore \text { Position vector of } R & =\frac{5 \overrightarrow{\mathrm{b}}-4 \overrightarrow{\mathbf{a}}}{5-4} \\ & =5 \overrightarrow{\mathrm{b}}-4 \overrightarrow{\mathbf{a}} \end{aligned} $$

Hence, the correct answer is option: 'A'.