The sum, difference and cross product of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are mutually perpendicular if

 $\overrightarrow{A}$ and $\overrightarrow{B}$ must be perpendicular to each other and $\left|\overrightarrow{A}\right|=\left|\overrightarrow{B}\right|$

 $\overrightarrow{A}$ and $\overrightarrow{B}$ are perpendicular to each other

 $\overrightarrow{A}$ and $\overrightarrow{B}$ are perpendicular but their magnitudes are arbitrary 

$\left|\overrightarrow{A}\right|=\left|\overrightarrow{B}\right|$ and their directions are arbitrary