Answer
$\theta=50^{\circ}$
The two vectors are not orthogonal.
Work Step by Step
Here, we have $u=(2,1); v=(1,3)$
$|\overrightarrow{u}|=\sqrt {(2)^2+(1)^2}=\sqrt {5}$;
$|\overrightarrow{u}|=\sqrt {(1)^2+(3)^2}=\sqrt {10}$;
$\overrightarrow{u} \cdot \overrightarrow{v}=2(1)+1(3)=5$
The angle $\theta$ can be calculated as:
$\cos \theta=\dfrac{\overrightarrow{u} \cdot \overrightarrow{v}}{|\overrightarrow{u}| |\overrightarrow{v}|}$
This implies that
$\cos \theta=\dfrac{5}{|\sqrt {5}| |\sqrt {10}|}=0.707$
Thus,
$\theta=\cos^{-1} (0.707) \approx 50^{\circ}$
Hence, the two vectors are not orthogonal.
