Answer
$(\frac{-1}{\sqrt{10}},\frac{3}{\sqrt{10}})$
Work Step by Step
The unit vector in the direction of v is $ v/||v|| = (v_1,v_2)/||(v_1,v_2)|| = $$(-5,15)/\sqrt{(-5)^2+15^2}$ =$(\frac{-5}{\sqrt{250}},\frac{15}{\sqrt{250}})$ = $(\frac{-5}{5\sqrt{10}},\frac{15}{5\sqrt{10}}) = (\frac{-1}{\sqrt{10}},\frac{3}{\sqrt{10}})$ , which is of length one from definition of unit vector.