Answer
If $u$ and $v$ are the diagonals of a rhombus, then $u\cdot v=0$
Work Step by Step
A rhombus can be formed by joining the points $(-a,0),(0,b),(a,0),(0,-b)$
The vectors from $(-a,0)$ to $(a,0)$ and from $(0,-b)$ to $(0,b)$ are the diagonals.
The vector from $(-a,0)$ to $(a,0)$:
$u=[a-(-a)]i+(0-0)j=2a~i$
The vector from $(0,-b)$ to $(0,b)$:
$v=(0-0)i+[b-(-b)]j=2b~j$
$u\cdot v=2a~i\cdot 2b~j=0$
Hence, $u$ and $v$ are perpendicular.
