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Найди угол \(\alpha \) между векторами \(\overline{a} \) и \(\overline{b} \) , если:

1. \(|\overline{a} |=4\) , \(|\overline{b} |=8\) , \(\overline{a} \,\overline{b} =-16\) ;

2. \(|\overline{a} |=3\) , \(|\overline{b} |=12\) , \(\overline{a} \,\overline{b} =-18\sqrt{2}\) ;

3. \(|\overline{a} |=14\) , \(|\overline{b} |=5\) , \(\overline{a} \,\overline{b} =-35\sqrt{3}\) .

Решение.

1. \(\cos \alpha =\) [ ]. Следовательно, \(\alpha =180\degree -\) [ ] \(\degree =\) [ ] \(\degree \) .

2. \(\cos \alpha =\) [ ]. Следовательно, \(\alpha =180\degree -\) [ ] \(\degree =\) [ ] \(\degree \) .

3. \(\cos \alpha =\) [ ]. Следовательно, \(\alpha=180\degree -\) [ ] \(\degree =\) [ ] \(\degree \) .

Ответ:

1. [ ] \(\degree \) ; 2) [ ] \(\degree \) ; 3) [ ] \(\degree \) .