Answer
$$\left\langle\frac{1}{\sqrt 5},-\frac{2}{\sqrt 5}\right\rangle.$$
Work Step by Step
The unit vector in the direction opposite to $ v $ is given by
$$-e_v= -\frac{v}{\|v\|}=-\frac{\left\langle-2,4\right\rangle}{\sqrt{4+16}}=\left\langle\frac{2}{2\sqrt 5},-\frac{4}{2\sqrt 5}\right\rangle.$$
Simplifying, we get:
$$\left\langle\frac{1}{\sqrt 5},-\frac{2}{\sqrt 5}\right\rangle.$$
