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Question: If position vectors of a point A is **a** + 2**b** and **a** divides AB in the ratio \(2:3\), then t...

If position vectors of a point A is a + 2b and a divides AB in the ratio 2:32:3, then the position vector of B is

A

2a – b

B

b – 2a

C

a – 3b

D

b

Answer

a – 3b

Explanation

Solution

If x be the position vector of B, then a divides AB in the ratio 2 : 3.

a=2x+3(a+2b)2+3a = \frac{2x + 3(a + 2b)}{2 + 3}

⇒ 5a−3a−6b=2x⇒x=a−3b.5a - 3a - 6b = 2x \Rightarrow x = a - 3b.