
\begin{enumerate}
\item $\vv{u}\dbinom{-1}{2}$ et $\vv{v}\dbinom{3}{-5}$.
\[
\vv{u}\cdot\vv{v}=xx'+yy'=(-1)\times3+2\times(-5)=-13.
\]

Ainsi,

\[
\cos\big(\vv{u}\mathpunct{},\mathpunct{}\vv{v}\big)=\dfrac{\vv{u}\cdot\vv{v}}{\|\vv{u}\|\times\|\vv{v}\|}=\dfrac{-13}{\sqrt{5}\times\sqrt{34}}=\dfrac{-13}{\sqrt{170}}\;,
\]

soit :

\[
\boxed{\big(\vv{u}\mathpunct{},\mathpunct{}\vv{v}\big)\approx177\degres.}
\]

\item $\vv{u}\dbinom{3}{4}$ et $\vv{v}\dbinom{5}{6}$.
\[
\vv{u}\cdot\vv{v}=xx'+yy'=3\times5+4\times6=39.
\]

Ainsi,

\[
\cos\big(\vv{u}\mathpunct{},\mathpunct{}\vv{v}\big)=\dfrac{\vv{u}\cdot\vv{v}}{\|\vv{u}\|\times\|\vv{v}\|}=\dfrac{39}{5\times\sqrt{61}}\;,
\]

soit :

\[
\boxed{\big(\vv{u}\mathpunct{},\mathpunct{}\vv{v}\big)\approx3\degres.}
\]

\item $\vv{u}\dbinom{0}{2}$ et $\vv{v}\dbinom{-1}{5}$.
\[
\vv{u}\cdot\vv{v}=xx'+yy'=10.
\]

Ainsi,

\[
\cos\big(\vv{u}\mathpunct{},\mathpunct{}\vv{v}\big)=\dfrac{\vv{u}\cdot\vv{v}}{\|\vv{u}\|\times\|\vv{v}\|}=\dfrac{10}{2\times\sqrt{26}}\;,
\]

soit :

\[
\boxed{\big(\vv{u}\mathpunct{},\mathpunct{}\vv{v}\big)\approx11\degres.}
\]

\item $\vv{u}\dbinom{2}{0}$ et $\vv{v}\dbinom{-1}{5}$.
\[
\vv{u}\cdot\vv{v}=xx'+yy'=-2.
\]

Ainsi,

\[
\cos\big(\vv{u}\mathpunct{},\mathpunct{}\vv{v}\big)=\dfrac{\vv{u}\cdot\vv{v}}{\|\vv{u}\|\times\|\vv{v}\|}=\dfrac{-1}{\sqrt{26}}\;,
\]

soit :

\[
\boxed{\big(\vv{u}\mathpunct{},\mathpunct{}\vv{v}\big)\approx101\degres.}
\]
\end{enumerate}
