Answer
$$ e=\langle \cos \frac{4 \pi }{7}, \sin \frac{4 \pi }{7}\rangle.$$
Work Step by Step
A unit vector $ e $ making an angle of $\frac{4 \pi }{7}$ with the x-axis is given by $$ e=\langle \cos \frac{4 \pi }{7}, \sin \frac{4 \pi }{7}\rangle.$$
