I was doing some 2D vector practices and came across a problem.
https://i.stack.imgur.com/VMUT6.png (I'm not yet allowed to embed a picture so here's a link)
I was asked to find the vector AQ and my answer was
AB + AC
= b - a - c + a
= b - c
But the answer is - a + 1/2(b) + 1/2 c
$$\vec{AQ}=\frac{1}{2}(\vec{AB}+\vec{AC})=\frac{1}{2}[(\vec b -\vec a)+(\vec c-\vec a)]=\frac{1}{2}\vec b+\frac{1}{2}\vec c-\vec a$$
Note that $\vec{AB}+\vec{AC}$ in the diagonal of the parallelogram with sides $\vec{AB}$ and $\vec{AC}$. $\vec{AQ}$ is just half of that.