Answer
$135^{\circ}$
Work Step by Step
$\textbf u $=$\langle 2,1 \rangle$
$\textbf v $=$\langle -3,1 \rangle$
$\cos\theta$=$\frac{ \textbf u . \textbf v }{ | \textbf u | | | \textbf v | } $
$\cos\theta$=$\frac{ \langle 2,1 \rangle . \langle -3,1 \rangle }{ | \sqrt {2^2+1^1}| | | \sqrt { (-3)^2+1^2} | } $
$\cos\theta$=$\frac{ 2\times (-3)+1\times 1 }{ | \sqrt {2^2+1^1}| | | \sqrt { (-3)^2+1^2} | } $
$\cos\theta$=$\frac{ -5 }{ | \sqrt {5}| | | \sqrt { 10} | } $
$\cos\theta$=$\frac{ -5 }{ \sqrt {50} }=\frac{-5}{5\sqrt 2}=-\frac{1}{\sqrt 2}$
$\theta$ $=\cos^{-1}\left(-\frac{1}{\sqrt 2}\right)=135^{\circ}$
