If P, Q, R divide the sides BC, CA and AB of `DeltaABC` in the same ratio, prove that the centroid of the triangles `ABC and PQR` coincide.

If D(2,1,0) ,E(2,0,0) and F(0,1,0) are mid points of the sides BC,CA and AB of triangle ABC respectively, then the centroid of triangle ABC is

Points L,M,N divide the sides BC,CA,AB of Delta ABC in the ratio 1:4,3:2,3:7 respectively.Prove that vec AL+vec BM+vec CN is a vector parallel to vec CK where K divides AB in the ratio 1:3

A(1,3),B(4,-1),C(-8,4) are the vertices of a triangle ABC. If D,E,F divides BC,CA,AB in the same ratio 2:1 then centroid of triangle DEF is

SIDES The three line segments 'AB BC and CA' that form the triangle 'ABC are called the sides of the triangles 'ABC.

In triangleABC, if the points P, Q, R divides the sides BC, CA, AB in the ratio 1:4, 3:2, 3:7 respectively and the point S divides side AB in the ratio 1:3, then (overline(AP)+overline(BQ)+overline(CR)):(overline(CS)) =