In my math book there is an example:
What is the sum of $ \overrightarrow{MA} + \overrightarrow{MB}+ \overrightarrow{MC}= \overrightarrow{O}$ considering the picture below:
The answer is: $3\overrightarrow{MM}=0$
How does the author get this answer? I set $\overrightarrow{AB}=\overrightarrow{a}$ and $\overrightarrow{AC}=\overrightarrow{b}$ and calculated that it is really $\overrightarrow{0}$.
Is there a simpler and quicker way if dealing with $\overrightarrow{MA}, \overrightarrow{MB}, \overrightarrow{MC}$?
Give that the midpoint of $AB$ is $D$ extend $MD$ outside triangle to point $E$ where $MD=DE$, then $MC=EM$. so consider $\overrightarrow{MA}+\overrightarrow{MB}+\overrightarrow{MC}$ as $\overrightarrow{MB}+\overrightarrow{BE}+\overrightarrow{EM}=\overrightarrow{0}$.