Answer
$1.0799rad=61.87^\circ$
Work Step by Step
$\mathbf{u}=<1,1,1>\hspace{10mm}\mathbf{v}=<2,1,-1>$
$\mathbf{u}\cdot\mathbf{v}=1\times2+1\times1+1\times(-1)=2+1-1=2$
$\|\mathbf{u}\|=\sqrt{1^2+1^2+1^2}=\sqrt{3}$
$\|\mathbf{v}\|=\sqrt{2^2+1^2+(-1)^2}=\sqrt{6}$
$\theta=\cos^{-}\left(\frac{\mathbf{u}\cdot\mathbf{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}\right)=\cos^{-1}\left(\frac{2}{\sqrt{3}\sqrt{6}}\right)=\cos^{-1}\left(\frac{2}{3\sqrt{2}}\right)=\cos^{-1}\left(\frac{\sqrt{2}}{3}\right)=1.0799rad=61.87^\circ$
