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Position Vector

A and B are t...

Question

A and B are two points with position vectors $2 \to a - 3 \to b$ and $6 \to b - \to a$ respectively. Write the position vector of a point P which divides the line segment AB internally in the ratio 1:2.

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Solution

Given: $- - \to O A = 2 \to a - 3 \to b$

$- - \to O B = 6 \to b - \to a$

Since P divides AB in 1:2 internally, so, $- - \to O P = \frac{1. - - \to O B + 2. - - \to O A}{1 + 2} = \frac{1. (6 \to b - \to a) + 2. (2 \to a - 3 \to b)}{1 + 2}$

Therefore, $- - \to O P = \frac{3 \to a}{3} = \to a$

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