Question

The position vectors of points P and Q are `overset->p and overset->q` respectively. The point R divides line segment PQ in the ratio 3 : 1 and S is the mid-point of line segment PR. The position vector of S is ______.

Options

• `(overset->p + 3overset->q)/4`

• `(overset->p + 3overset->q)/8`

• `(5overset->p + 3overset->q)/4`

• `(5overset->p + 3overset->q)/8`

Answer 1

The position vectors of points P and Q are `overset->p and overset->q` respectively. The point R divides line segment PQ in the ratio 3 : 1 and S is the mid-point of line segment PR. The position vector of S is `underlinebb((5overset->p + 3overset->q)/8)`.

Explanation:

Position vector of R,

`overset->r = (3overset->q + overset->p)/(3 + 1)`

or   `overset->r = (3overset->q + overset->p)/(4)`

Given S is the mid-point of PR 

∴ Position vector of S, 

`overset->S = (overset->p + overset->r)/2`

= `(overset->p((3overset->q  +  overset->p)/4))/2`

= `(5overset->p + 3overset->q)/8`