Answer
$108.43^{\circ}$
Work Step by Step
We know that the angle between two vectors is:
$\theta =\cos^{-1} [ \dfrac{u \cdot v}{||u|| \space ||v|| }]$
Therefore, $||u||=\sqrt{6^2+3^2}=\sqrt{45}$ and $||v||=\sqrt{(-4)^2+(4)^2}= 4\sqrt {2}$
$\theta =\cos^{-1} [ \dfrac{(6)(-4)+(3)(4)}{ \sqrt{45} 4\sqrt {2}}]=\cos^{-1}[\dfrac{-12}{\sqrt{45}(4 \sqrt 2)}]$
So, $\theta =108.43^{\circ}$
