How would you prove that given two 2D vectors in the $\vec{v} = \begin{bmatrix} v_{1} \\ v_{2} \\ \end{bmatrix}$ and $\vec{u} = \begin{bmatrix} u_{1} \\ u_{2} \\ \end{bmatrix}$
Then the sign of the dotproduct $ \vec{u}\cdot \vec{v}$.
Meaning in the following situation.
$\begin{matrix} \vec{u}\cdot \vec{v} < 0 \\ \vec{u}\cdot \vec{v} > 0 \\ \vec{u}\cdot \vec{v} = 0 \end{matrix}$
Directly influences the size of the angle $\theta$ between the vector?
where the dot product in 2d is defined. $\vec{u}\cdot \vec{v} =|\vec{u}|\cdot |\vec{v}| \cdot cos(\theta) $
It can simply be that the dot product is negativ if the angle is larger $\theta < 180 ^\circ$ and dotproduct is zero if the angle betwen the vector is 90 $^\circ$ and so on?
