Chapter 5.1, Problem 11E

Considerthevector $\stackrel{\to }{u}=\left[\begin{array}{l}1\\ 3\\ ⋮\\ 1\end{array}\right]$ and $\stackrel{\to }{v}=\left[\begin{array}{l}1\\ 0\\ ⋮\\ 0\end{array}\right]$ in ${ℝ}^n$ .
a. For $n=2,3,4$ , find the angle $\theta$ between $\stackrel{\to }{u}$ and $\stackrel{\to }{v}$ .For $n=2$ and 3, represent the vectors graphically.
b. Find the limit of $\theta$ as n approaches infinity.