It is important to know that the vector v = 3i + j refers to a horizontal coordinate of 3 and a vertical coordinate of 1. The image below shows the vector
To find the magnitude, we use the following formula
[tex]\begin{gathered} |v|=\sqrt[]{x^2+y^2}=\sqrt[]{3^2+1^2}=\sqrt[]{9+1} \\ |v|=\sqrt[]{10} \end{gathered}[/tex]