In $\triangle{ABC}$, Prove $\vec{AB} + \vec{AC} = 2\vec{AD}$

Question

In a triangle $\triangle{ABC}$, $D$ is the center of $BC$.Prove that $\vec{AB} + \vec{AC} = 2\vec{AD}$

I just get these equation from the triangle

$\vec{AB} + \vec{BD} = \vec{AD}$

$\vec{AD} + \vec{DC} = \vec{AC}$

$\vec{AB} + \vec{BC} = \vec{AC}$

I have just started vector without any previous experience.Please answer with explanation.

Answer 1

You're almost done. Note that$\vec{BD}$ are $\vec{DC}$ same. Simply subtract the second equation from the first one. Or, do the following:

$\vec{BD} = \vec{AD} -\vec{AB}$

$\vec{DC} = \vec{AC} -\vec{AD}$

Write $\vec{BD}= \vec{DC}.$ Can you continue?