Answer
$\frac{-3}{\sqrt{58}}i+\frac{7}{\sqrt{58}}j$
Work Step by Step
Let $\mathbf v=-3i+7j$. We can obtain a unit vector in the same direction as $\mathbf v$ by multiplying $\mathbf v$ by $\frac{1}{|\mathbf v|}$.
By definition, $|\mathbf v|=\sqrt{(-3)^2+7^2}=\sqrt{9+49}=\sqrt{58}$.
So $\frac{\mathbf v}{|\mathbf v|}=\frac{\mathbf v}{\sqrt{58}}=\frac{-3i+7j}{\sqrt{58}}=\frac{-3}{\sqrt{58}}i+\frac{7}{\sqrt{58}}j$ is a unit vector in the same direction as $\mathbf v$.
