I don't understand how to solve this problem, help please.

Quote:

The Vectors $\displaystyle U = cos\theta I+sin\theta J, V = -sin\theta I+cos\theta J$ for any $\displaystyle \theta $, form an orthonormal basis for the plane; they are orthogonal vector of length 1. Let $\displaystyle \theta = \frac{2\pi}{4} $ and $\displaystyle x = 5I+8J$. Then we can write $\displaystyle X = uU + vV$

with $\displaystyle u$ = ___, $\displaystyle v$ = ___