If `vec(a)` and `vec(b)` are the position vectors of two points `A` and `B`, then the
position vector `vec(c)` of a point `P` dividing `AB` in the ratio `m: n` is given by

`vec(c)= (m vec(b) + n vec(a))/(m+n)`

`text(Particular Case : )`
`1. ` Position vector of the mid point of `AB` is `(vec(a) +vec(b))/2`

`2.` If the point `P` divides `AB` in the ratio `m: n` externally, then p.v. of `P` is given by ` vec(c)= (mvec(b)-nvec(a))/(m-n)`

`text(Using section Formulae we can prove that :)`

`1.` p. v. of the centroid of a tnangle `ABC = (vec(alpha)+vec(beta)+vec(gamma))/3`

(Concurrency of medians)

`2.` p.v. of incentre of the `Delta = (avec(alpha)+bvec(beta)+cvec(gamma))/(a+b+c)`

(Concurrency of internal angle bisectors)

Excentres of the `Delta ` are `(-avec(alpha)+bvec(beta)+cvec(gamma) )/(-a+b+c) ; (avec(alpha)-bvec(beta)+cvec(gamma) )/(a-b+c)` and `(avec(alpha)+bvec(beta)-cvec(gamma) )/(a+b-c)`

`3.` p.v. of circumcentre of the `Delta = (vec(alpha) sin 2A+vec(beta) sin 2 B+vec(gamma)sin2C)/(sum sin 2A)`
(Concurrency of perpendicular bisectors of sides)

`4.` p.v. of orthocenter of the `Delta = (vec(a) tan A+ vec(b) tan B+ vec(c)tan C)/(sum tan A)`

(Concurrency of altitudes)