Question

Find the position vector of point R which divides the line joining the points P and Q whose position vectors are `2hati - hatj + 3hatk`  and `- 5hati + 2hatj - 5hatk` in the ratio 3:2 is internally.

Answer 1

It is given that the points P and Q have position vectors `barp = 2hati - hatj + 3hatk` and `barq = - 5hati + 2hatj - 5hatk` respectively.

If R(`barr`) divides the line segment PQ internally in the ratio 3:2, by section formula for internal division,

`barr = (3q + 2p)/(3 + 2)`

= `(3 (- 5hati + 2hatj - 5hatk) + 2(2hati - hatj + 3hatk))/5`

= `(- 11hati + 4hatj - 9hatk)/5`

= `1/5(- 11hati + 4hatj - 9hatk)`

∴ Coordinates of R = `(- 11/5, 4/5, -9/5)`

Hence, the position vector of R is `1/5(- 11hati + 4hatj - 9hatk)` and the coordinates of R are `(- 11/5, 4/5, -9/5)`