Question

$If$ $\overrightarrow{AD},\overrightarrow{BE},\overrightarrow{CF}$ are medians of an equilateral triangle $ABC$, then $\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF}$ equals to

• A. $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}$
• B. a zero vector
• C. both $1$ and $2$
• D. $2\overrightarrow{AF}+3\overrightarrow{BF}$

Answer 1

The correct option is C both $1$ and $2$

The question wants to ask what is the vector sum of these $23$ median vectors. The answer is correct. Let the vectors of vertices be $a,b$ and $0$ then the median vectors are $(a+b)/2,b/2-a$ and $a/2-b$
The sum is a zero vector. and $a+b-a+(-b)$ which is vector sum of $\overrightarrow{AB},\overrightarrow{BC}$ and $\overrightarrow{CA}$ is also $0$.