Find the unit vector that has the same direction as the vector v. v = 3i + j(answer choices are pictured below)

[tex]\bf \textit{unit vector for \underline{v}}\qquad v=\ \textless \ a,b\ \textgreater \ \implies \stackrel{unit~vector}{\cfrac{a}{\sqrt{a^2+b^2}}~,~\cfrac{b}{\sqrt{a^2+b^2}}}\\\\ -------------------------------\\\\ v=3i+j\implies v=\ \textless \ 3,1\ \textgreater \ \implies \stackrel{unit~vector}{\cfrac{3}{\sqrt{3^2+1^2}}~,~\cfrac{1}{\sqrt{3^2+1^2}}} \\\\\\ \left( \cfrac{3}{\sqrt{10}}~,~\cfrac{1}{\sqrt{10}} \right)[/tex]