Given $ABCD$ is a rhombus and diagonals intersect at $E$Since in a rhombus diagonals bisect each other$|\vec{EA}|=|\vec{EC}|\;\text{ and }\;|\vec{EB}|=|\vec{ED}|$but since they are opposite to each other they are of opposite signs $\Rightarrow \vec{EA} = -\vec{EC}$ and $\vec{EB} = -\vec{ED}$$\Rightarrow \vec{EA} + \vec{EC} = \vec{O}$...(i) and $\vec{EB} + \vec{ED} = \vec{O}$Add (1) and (2)$\Rightarrow \vec{EA} + \vec{EB} + \vec{EC} + \vec{ED} = \vec{O}$