\({\left( {\overrightarrow u .\;\overrightarrow v } \right)^2} = {\left( {\overrightarrow u } \right)^2}.{\left( {\overrightarrow v } \right)^2}\)\( \Leftrightarrow {\left[ {\left| {\overrightarrow u } \right|.\;\left| {\overrightarrow v } \right|.\cos \;\left( {\overrightarrow u ,\;\overrightarrow v } \right)} \right]^2} = {\left| {\overrightarrow u } \right|^2}.{\left| {\overrightarrow v } \right|^2}\)
\(\begin{array}{l} \Leftrightarrow {\left[ {\cos \;\left( {\overrightarrow u ,\;\overrightarrow v } \right)} \right]^2} = 1\\ \Leftrightarrow \left[ \begin{array}{l}\cos \;\left( {\overrightarrow u ,\;\overrightarrow v } \right) = 1\\\cos \;\left( {\overrightarrow u ,\;\overrightarrow v } \right) = - 1\end{array} \right.\end{array}\)
\( \Leftrightarrow \left[ \begin{array}{l}\;\left( {\overrightarrow u ,\;\overrightarrow v } \right) = {0^o}\\\left( {\overrightarrow u ,\;\overrightarrow v } \right) = {180^o}\end{array} \right.\)
Hay hai vectơ \(\overrightarrow u ,\;\overrightarrow v \) cùng phương.
Vậy hai vectơ \(\overrightarrow u ,\;\overrightarrow v \) cùng phương thì \({\left( {\overrightarrow u .\;\overrightarrow v } \right)^2} = {\left( {\overrightarrow u } \right)^2}.{\left( {\overrightarrow v } \right)^2}\)
