Answer
$\hat{\vec v}= \frac{8}{17}i-\frac{15}{17}j$
Work Step by Step
Given $\vec v=8i-15j$, we have $||\vec v||=\sqrt {8^2+(-15)^2}=17$, thus we have the unit vector in the same direction $\hat{\vec v}=\frac{\vec v}{||\vec v||}=\frac{8}{17}i-\frac{15}{17}j$
