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Position Vector

The position ...

Question

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

A

5 b - 4 a

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B

5 b + 4 a

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C

4 b - 5 a

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D

4 b + 5 a

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Solution

The correct option is C $5 b - 4 a$
Given condition
$P R = 5 P Q$
$R - P = 5 (Q - P)$
$R = 5 Q - 5 P + P$
$R = 5 Q - 4 P$
$R = 5 b - 4 a$

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State True or False.

The following position vectors are collinear.

3 a - 4 b + 3 c

- 4 a + 5 b - 6 c

4 a - 7 b + 6 c

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