The position vectors of the points A-B and C are respectively a-b and c- If P divides AB in the ratio 3-4 and Q divides BC in the ratio 2-1 both externally- then PQ is

Given : nbsp;P divides AB in the ratio 3:4 ⇒OP=3OB 4OA3 4=3b 4a 1 OP=4a 3b Q divides nbsp;BC in the ratio 2:1 both externally. OQ=2OC OB2 1=2c b ∴PQ=2(c+b ...

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Byju's Answer

Standard XII

Physics

Introduction

The position ...

Question

The position vectors of the points $A, B$ and $C$ are respectively $\to a, \to b$ and $\to c .$ If $P$ divides $- - \to A B$ in the ratio $3 : 4$ and $Q$ divides $- - \to B C$ in the ratio $2 : 1$ both externally, then $- - \to P Q$ is

(\to c + \to b - \to a)

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(4 \to a - \to c - \to b)

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2 (\to c + \to b - 2 \to a)

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(\to c + \to b - 2 \to a)

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Solution

The correct option is C $2 (\to c + \to b - 2 \to a)$
Given : $P$ divides $- - \to A B$ in the ratio $3 : 4$
$\Rightarrow - - \to O P = \frac{3 - - \to O B - 4 - - \to O A}{3 - 4} = \frac{3 \to b - 4 \to a}{- 1}$
$- - \to O P = 4 \to a - 3 \to b$

$Q$ divides $- - \to B C$ in the ratio $2 : 1$ both externally.
$- - \to O Q = \frac{2 - - \to O C - - - \to O B}{2 - 1} = 2 \to c - \to b$
$∴ - - \to P Q = 2 (\to c + \to b - 2 \to a)$

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The position vectors of the points A,B and C are respectively →a,→b and →c. If P divides −−→AB in the ratio 3:4 and Q divides −−→BC in the ratio 2:1 both externally, then −−→PQ is

The position vectors of the points $A, B$ and $C$ are respectively $\to a, \to b$ and $\to c .$ If $P$ divides $- - \to A B$ in the ratio $3 : 4$ and $Q$ divides $- - \to B C$ in the ratio $2 : 1$ both externally, then $- - \to P Q$ is