Question

The three medians of triangle PQR meet at a common point G. The point G divides each median in a 2:1 ratio. Prove that vector GP + vector GQ + vector GR = 0 vector

Answer 1

let p,q,r be the position vectors of P Q and R respectively
then position vector of g=(p+q+r)/3

Answer 2

now vector GP = pv of P -pv of G= p-(p+q+r)/3
now vector GQ = pv of Q -pv of G= q-(p+q+r)/3
now vector GR = pv of R -pv of G= r-(p+q+r)/3

adding we have
vector GP + vector GQ + vector GR = (p+q+r)- 3*(p+q+r)/3
=(p+q+r) - (p+q+r)=0 vector