Chapter 5 - Inner Product Spaces - 5.2 Inner Product Spaces - 5.2 Exercises - Page 246: 49

$$\cos \theta=\frac{1}{3}.$$

Let $p(x)=1-x+x^2,\quad q(x)=1+x+x^2, \quad \langle u, v\rangle=a_0b_0+a_1b_1+a_2b_2$. The angle $\theta$ between $u$ and $v$ is given by the formula $$\cos \theta=\frac{\langle u, v\rangle}{\|u\| \cdot\|v\|}=\frac{1-1+1}{\sqrt{ 1+1+1}\sqrt{ 1+1+1}}=\frac{1}{3}.$$