Khi nào thì (ecto u. vecto v)^2 = vecto u^2 . vecto v^2

Ta có: $\overrightarrow{u}.\overrightarrow{v}=\left|\overrightarrow{u}\right|.\left|\overrightarrow{v}\right|.c\text{os}\left(\overrightarrow{u},\overrightarrow{v}\right)$

$\iff {\left(\overrightarrow{u}.\overrightarrow{v}\right)}^2={\left[\left|\overrightarrow{u}\right|.\left|\overrightarrow{v}\right|.c\text{os}\left(\overrightarrow{u},\overrightarrow{v}\right)\right]}^2={\overrightarrow{u}}^2.{\overrightarrow{v}}^2.c{\text{os}}^2\left(\overrightarrow{u},\overrightarrow{v}\right)$

Để ${\left(\overrightarrow{u}.\overrightarrow{v}\right)}^2={\overrightarrow{u}}^2.{\overrightarrow{v}}^2$ thì $c{\text{os}}^2\left(\overrightarrow{u},\overrightarrow{v}\right)=1\iff \left[\begin{array}{l}c\text{os}\left(\overrightarrow{u},\overrightarrow{v}\right)=1\\ c\text{os}\left(\overrightarrow{u},\overrightarrow{v}\right)=-1\end{array}\right.\iff \left[\begin{array}{l}\left(\overrightarrow{u},\overrightarrow{v}\right)=0^0\\ \left(\overrightarrow{u},\overrightarrow{v}\right)={180}^0\end{array}\right.$

Vậy khi góc giữa hai vecto $\overrightarrow{u},\overrightarrow{v}$ là 0⁰ hoặc 180⁰ thì ${\left(\overrightarrow{u}.\overrightarrow{v}\right)}^2={\overrightarrow{u}}^2.{\overrightarrow{v}}^2.$