Chapter 5 - Inner Product Spaces - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 236: 75

$\left(\frac{5}{13},\frac{-12}{13}\right)$

Given $\mathbf{v}=(12,5)$, then the vector $u=(5,-12)$ is orthogonal to $v$. Now the unit vector indirection of $u$ and orthogonal to $v$ is $$\frac{u}{\|u\|}=\frac{(5,-12)}{\sqrt{25+144}}=\left(\frac{5}{13},\frac{-12}{13}\right).$$