3. Détermine l'angle $\theta$ formé par les vecteurs.
a) $\vec{u}=[-1,8]$ et $\vec{v}=[3,-5]$

Step 1 ：Find the dot product of the vectors \(\vec{u}\) and \(\vec{v}\): \(u \cdot v = (-1 * 3) + (8 * -5) = -43\)

Step 2 ：Find the magnitudes of the vectors \(\vec{u}\) and \(\vec{v}\): \(||u|| = \sqrt{(-1)^2 + 8^2} = 8.062\) and \(||v|| = \sqrt{3^2 + (-5)^2} = 5.831\)

Step 3 ：Use the formula to find the angle \(\theta\) between the vectors: \(\theta = \arccos{\frac{u \cdot v}{||u|| ||v||}}\)

Step 4 ：Plug in the values: \(\theta = \arccos{\frac{-43}{(8.062)(5.831)}}\)

Step 5 ：Calculate the angle in radians: \(\theta \approx 2.726\)

Step 6 ：Convert the angle to degrees: \(\theta \approx 156.16^\circ\)

Step 7 ：\(\boxed{\theta \approx 156.16^\circ}\)