a) Ta có:
\[\overrightarrow{u}.\;\overrightarrow{v} = \left|{\overrightarrow{u}}\right|.\;\left|{\overrightarrow{v}}\right|.\cos\left({\overrightarrow{u},\;\overrightarrow{v}}\right) = \left|{\overrightarrow{u}}\right|.\;\left|{\overrightarrow{v}}\right|\]
Suy ra \(\cos\left({\overrightarrow{u},\;\overrightarrow{v}}\right) = 1\), tức là \(\left({\overrightarrow{u},\;\overrightarrow{v}}\right) = 0^\circ\).
Vậy \(\overrightarrow{u}\) và \(\overrightarrow{v}\) cùng hướng.
b) Ta có:
\[\overrightarrow{u}.\;\overrightarrow{v} = \left|{\overrightarrow{u}}\right|.\;\left|{\overrightarrow{v}}\right|.\cos\left({\overrightarrow{u},\;\overrightarrow{v}}\right) = -\left|{\overrightarrow{u}}\right|.\;\left|{\overrightarrow{v}}\right|\]
Suy ra \(\cos\left({\overrightarrow{u},\;\overrightarrow{v}}\right) = -1\), tức là \(\left({\overrightarrow{u},\;\overrightarrow{v}}\right) = 180^\circ\).
Vậy \(\overrightarrow{u}\) và \(\overrightarrow{v}\) ngược hướng.
