Chapter 5 - Inner Product Spaces - 5.2 Inner Product Spaces - 5.2 Exercises - Page 246: 46

$$\cos \theta=0.$$ That is, $\theta=\frac{\pi}{2}$

Let $u=(\frac{1}{4},-1),\quad v=(2,1), \quad =2u_1v_1+u_2v_2$. The angle $\theta$ between $u$ and $v$ is given by the formula $$\cos \theta=\frac{\langle u,v \rangle }{\|u\| \cdot\|v\|}=\frac{1-1}{\sqrt{ \frac{1}{8}+1}\sqrt{ 8+1}}=0.$$ That is, $\theta=\frac{\pi}{2}$