Answer
$(\frac{1}{\sqrt{17}},\frac{4}{\sqrt{17}})$
Work Step by Step
The unit vector in the direction of v is $ v/||v|| = (v_1,v_2)/||(v_1,v_2)|| = $$(3,12)/\sqrt{3^2+12^2}$ =$(\frac{3}{\sqrt{153}},\frac{12}{\sqrt{153}})$ = $(\frac{3}{3\sqrt{17}},\frac{12}{3\sqrt{17}}) = (\frac{1}{\sqrt{17}},\frac{4}{\sqrt{17}})$ , which is of length one from definition of unit vector.