Q8: $\overrightarrow{EA} + \overrightarrow{EB} + \overrightarrow{EC} + \overrightarrow{ED}$ for a rhombus $ABCD$

A rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other. So $EA = EC$ and $EB = ED$ in length.

$\overrightarrow{EA}$ and $\overrightarrow{EC}$ have the same length but point in opposite directions along $AC$⁠. A vector with the same length and the opposite direction is the negative, so $\overrightarrow{EC} = -\overrightarrow{EA}$⁠.

In the same way, along $BD$⁠, $\overrightarrow{ED} = -\overrightarrow{EB}$⁠.

Each vector cancels its negative: $\vec a + (-\vec a) = \vec 0$⁠.

Watch out: a sum of vectors is the zero vector $\vec 0$⁠, not the number 0. Options (b), (c) and (d) are non-zero vectors, because $A \ne D$ and $B \ne D$⁠.