In Exercise 20, let $V = P_2$ with inner product $$\langle p, q\rangle = \sum_{i=0}^2 p_i q_i$$
a. Find the distance between the vectors $p$ and $q$. b. Find the cosine of the angle between the vectors $p$ and $q$.
- $p(x) = x − 3$, $q(x) = 2x − 6$
The solution listed gives the distance as the radical of 10 and the cosine as 1, but I don't understand why. Detailed steps for calculations would be appreciated as I am getting different answers from the solution manual which is very brief.
Thanks in advance