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 :

Question

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 :

Infinity Learn · Accepted Answer

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$$→ $$+$$ GA→$$) $$+$$ $$(G1$$ $$A1$$→ $$+$$ $$A1G1$$→$$)=3GG1$$ → $$+$$ $$0$$→ $$+$$ $$0$$→ $$=$$ $$3GG1$$→

$G is the centroid of the triangle ABC and if G, is the centroid of another$ $triangle A_{1} B_{1} C_{1}, then value of A \vec{A_{1}} + B \vec{B_{1}} + C \vec{C_{1}} is :$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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 :

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$G is the centroid of the triangle ABC and if G, is the centroid of another$ $triangle A_{1} B_{1} C_{1}, then value of A \vec{A_{1}} + B \vec{B_{1}} + C \vec{C_{1}} is :$