Answer
$\theta=36.87^{\circ}$
Work Step by Step
$\textbf u $=$3 \textbf i +4\textbf j $
$\textbf v $=$\textbf j $
$\cos\theta$=$\frac{ \textbf u . \textbf v }{ | \textbf u | | | \textbf v | } $
$\cos\theta$=$\frac{ (3 \textbf i +4\textbf j) \cdot \textbf j }{ | 3 \textbf i +4\textbf j | |\textbf j | } $
$\cos\theta$=$\frac{ 3\times 0+4 \times 1 }{ | \sqrt {3^2+4^2}| | | {\sqrt { 0^2+1^2} | } }$
$\cos\theta$=$\frac{ 4 }{ ( 5) (1) } =\frac{4}{5} $
$\theta$ $=\cos^{-1}\left(\frac{4}{5}\right)=36.87^{\circ}$
