A) \[\overset{\to }{\mathop{O}}\,\]
B) \[2\overset{\to }{\mathop{AB}}\,\]
C) \[2\overset{\to }{\mathop{GE}}\,\]
D) \[2\overset{\to }{\mathop{GC}}\,\]
E) \[\overset{\to }{\mathop{GA}}\,+\overset{\to }{\mathop{GB}}\,\]
Correct Answer: A
Solution :
Since, D, E and F are mid points of the sides\[\overrightarrow{BC},\overrightarrow{CA}\] and\[\overrightarrow{AB}\]respectively of the triangle ABC and G is the centroid of the triangle, Thus, G will also be centroid of\[\Delta DEF\]. Hence,\[\overrightarrow{GD}+\overrightarrow{GE}+\overrightarrow{GF}=\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}\] \[\overrightarrow{GA}+2\overrightarrow{GD}\] \[\overrightarrow{GA}-\overrightarrow{GA}=\overrightarrow{0}\] (\[\because \]G divides AC in the ratio\[2:1\])You need to login to perform this action.
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