A and B are two points. The position vector of A is 6 b-2 a . A point P divides the line AB in the ratio 1: 2. If a-b is its position vector, then the position vector of B is given by

Question

A and B are two points. The position vector of A is 6 b-2 a . A point P divides the line AB in the ratio 1: 2. If a-b is its position vector, then the position vector of B is given by (A) 7 a-15 b (B) 7 a+15 b (C) 15 a-7 b (D) 15 a+7 b

Tardigrade Admin · Accepted Answer

Let B be the point ( vecr) ∴ (1⋅ vecr+2(6 vecb-2 veca)/1+2)= veca- vecb ⇒ vecr+12 vecb-4 veca=3 veca-4 vecb <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/ad96fee22ea692e855688a6265dfa329-.jpeg" /> 6 vecb-2 veca ⇒ vecr=7 veca-15 vecb ∴ B is 7 veca-15 vecb

Q. A and B are two points. The position vector of A is $6 b - 2 a$ . A point P divides the line AB in the ratio 1 : 2. If $a - b$ is its position vector, then the position vector of B is given by

$7 a - 15 b$

$7 a + 15 b$

$15 a - 7 b$

$15 a + 7 b$

Let $B$ be the point $(r)$
$∴ \frac{1 \cdot r + 2 ( 6 b - 2 a )}{1 + 2} = a - b$
$\Rightarrow r + 12 b - 4 a = 3 a - 4 b$

$6 b - 2 a$
$\Rightarrow r = 7 a - 15 b$
$∴ B$ is $7 a - 15 b$

Q. A and B are two points. The position vector of A is 6b−2a . A point P divides the line AB in the ratio 1 : 2. If a−b is its position vector, then the position vector of B is given by

7a−15b

7a+15b

15a−7b

15a+7b