G is the centroid of the triangle ABC and if G, is the centroid of another triangle A1B1C1, then value of AA1→+BB1→+CC1→ is :
G G→1
0
3 G G→1
None of these
Clearly AA1→=AG→+GG1→+G1A1→
B B1→ = BG→ + GG→1 +G1 B1→
CC1→ = CG→ + GG1→ + G1C1→
Adding these __,AA1→+BB1→+CC1→
=3GG1→ + (AG→ + BG→ + CG→) + (G1 A1→ + G1B1→ + G1C1→)
=3GG1→ + (AG→ + 2DG→) + (G1 A1→ + 2G1D1→)
(where AD and A1D1 are medians of the triangles ABC and A1B1C1 respectively.)
=3GG1→ + (AG→ + GA→) + (G1 A1→ + A1G1→)
=3GG1 → + 0→ + 0→ = 3GG1→