Giải thích các bước giải:
Ta có:
AC là đường chéo nên:
$\vec{AC}=\vec{AB}+\vec{AD}$
Ta có:
$m^2+n^2=2.(a^2+b^2)$
<=>$\vec{BC}^2+\vec{AC}^2=2.(\vec{AB}^2+\vec{BC}^2)$
<=>$\vec{BC}^2+(\vec{AB}+\vec{AD})^2=2.(\vec{AB}^2+\vec{BC}^2)$
<=>$\vec{BC}^2+(\vec{AB}+\vec{BC})^2=2.(\vec{AB}^2+\vec{BC}^2)$
<=>$\vec{BC}^2+\vec{AB}^2+2.\vec{AB}.\vec{BC}+\vec{BC}^2=2\vec{AB}^2+2\vec{BC}^2$
<=>$\vec{-AB}^2+2.\vec{AB}.\vec{BC}=0$
<=>$-(\vec{AC}-\vec{BC})^2+2.(\vec{AC}-\vec{BC}).\vec{BC}=0$