question_answer

If D, E and F are the mid points of the sides \[\overset{\to }{\mathop{BC}}\,,\text{ }\overset{\to }{\mathop{CA}}\,\] and\[\overset{\to }{\mathop{AB}}\,\]respectively of the triangle ABC and G is the centroid of the triangle, then \[\overset{\to }{\mathop{GD}}\,+\overset{\to }{\mathop{GE}}\,+\overset{\to }{\mathop{GF}}\,\]is

A)  \[\overset{\to }{\mathop{O}}\,\]           

B)        \[2\overset{\to }{\mathop{AB}}\,\]

C)  \[2\overset{\to }{\mathop{GE}}\,\]                      

D)        \[2\overset{\to }{\mathop{GC}}\,\]

E)  \[\overset{\to }{\mathop{GA}}\,+\overset{\to }{\mathop{GB}}\,\]