Chapter 5.1, Problem 38E

Consider three unit vectors ${\stackrel{\to }{v}}_1,{\stackrel{\to }{v}}_2$ , and ${\stackrel{\to }{v}}_3$ in ${ℝ}^n$ . We are told that ${\stackrel{\to }{v}}_1\cdot {\stackrel{\to }{v}}_2={\stackrel{\to }{v}}_1\cdot {\stackrel{\to }{v}}_3=1/2$ . What arethe possible values of ${\stackrel{\to }{v}}_2\cdot {\stackrel{\to }{v}}_3$ ? What could the angle between thevectors ${\stackrel{\to }{v}}_2$ and ${\stackrel{\to }{v}}_3$ be? Giveexamples: draw sketches forthe cases $n=2$ and $n=3$ .