Answer
$1.713$ rad = $98.13^\circ$
Work Step by Step
$\mathbf{u}=3\mathbf{i}+\mathbf{j}$ and $\mathbf{v}=-2\mathbf{i}+4\mathbf{j}$
$\mathbf{u}\cdot\mathbf{v}=3\times(-2)+1\times4=-6+4=-2$
$\|\mathbf{u}\|=\sqrt{3^2+1^2}=\sqrt{10}$ and $\|\mathbf{v}\|=\sqrt{(-2)^2+4^2}=\sqrt{20}=2\sqrt{5}$
${\theta}=\cos^{-1}\frac{\mathbf{u}\cdot\mathbf{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}=\cos^{-1}\frac{-2}{2\sqrt{10}\sqrt{5}}=\cos^{-1}{-\frac{\sqrt{2}}{10}}=1.713$ rad = $98.13^\circ$
