Answer
$\theta=78.93^{\circ}$
Work Step by Step
$\textbf u $=$-5 \textbf i +12\textbf j $
$\textbf v $=$ 3 \textbf i +2 \textbf j $
$\cos\theta$=$\frac{ \textbf u . \textbf v }{ | \textbf u | | | \textbf v | } $
$\cos\theta$=$\frac{ (-5\textbf i +12\textbf j ) \cdot (3 \textbf i+2 \textbf j) }{ | -5 \textbf i +12\textbf j | | 3 \textbf i + 2\textbf j | } $
$\cos\theta$=$\frac{ -5\times 3+12 \times 2 }{ | \sqrt {(-5)^2+12^2}| | | {\sqrt { 3^2+2^2} | } }$
$\cos\theta$=$\frac{ 9 }{ ( 13) (\sqrt {13}) } $
$\theta$ $=\cos^{-1}\left(\frac{9}{13\sqrt {13}}\right)=78.93^{\circ}$
