Chapter 5 - Inner Product Spaces - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 236: 76

$\left(\frac{15}{17},\frac{-8}{17}\right).$

Given $\mathbf{v}=(8,15)$, then the vector $u=(15,-8)$ is orthogonal to $v$. Now the unit vector indirection of $u$ and orthogonal to $v$ is $$\frac{u}{\|u\|}=\frac{(15,-8)}{\sqrt{25+144}}=\left(\frac{15}{17},\frac{-8}{17}\right).$$