Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.3 Geometric Sequences; Geometric Series - 12.3 Assess Your Understanding - Page 827: 112

$\dfrac{8}{17}i-\dfrac{15}{17}j$

If $v=ai+bj$, then the unit vector $u$ in the direction of $v$ is $u=\dfrac{v}{||v||}$, where $||v||=\sqrt{a^2+b^2}.$ Note that here, $||v||=\sqrt{8^2+(-15)^2}=\sqrt{289}=17$ Hence $u=\dfrac{8i-15j}{17}\\ u=\dfrac{8}{17}i-\dfrac{15}{17}j$