Question

P and Q are two points with position vectors `2overlinea + overlineb` and `overlinea - 3overlineb` respectively. The position vector of the point R which divides the line segment PQ in the ratio 1 : 2 externally is ______ 

Options

• `3overlineb`

• `4overlineb`

• `3overlinea + 4overlineb`

• `3overlinea + 5overlineb`

Answer 1

P and Q are two points with position vectors `2overlinea + overlineb` and `overlinea - 3overlineb` respectively. The position vector of the point R which divides the line segment PQ in the ratio 1 : 2 externally is `underline(3overlinea + 5overlineb)`.

Explanation:

Let R`(overliner)` divide line segment PQ externally in the ratio 1 : 2.

∴ `overliner = (-1(overlinea - 3overlineb) - 2(2overlinea + overlineb))/(1 - 2)`

= `3overlinea + 5overlineb`