Question

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

• A. $5b–4a$
• B. $5b+4a$
• C. $4a-5b$
• D. $4a+5b$

Answer 1

The correct option is A

$5b–4a$

Explanation for the correct option:

Find the position vector of given vector

In the question, two-position vectors of two points $P$ and $Q$ are $a$ and $b$ respectively are given.

Since the distance between the position vector $x$ and $y$ is given by $x-y$.

It is given that, $PR=5PQ$.

Therefore,

$$\begin{gathered} P-R=5\left(P-Q\right) \\ \Rightarrow a-R=5(a-b) \\ \Rightarrow R=a-5(a-b) \\ \Rightarrow R=5b-4a \end{gathered}$$

Therefore, the position vector $R$ is $5b–4a$.

Hence, option $A$, $5b–4a$ is the correct answer.