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

1. \(|\overline{a} |=8\) , \(|\overline{b} |=5\) , \(\overline{a} \,\overline{b} =20\) ;

2. \(|\overline{a} |=3\) , \(|\overline{b} |=4\) , \(\overline{a} \,\overline{b} =6\sqrt{3}\) ;

3. \(|\overline{a} |=7\) , \(|\overline{b} |=6\) , \(\overline{a} \,\overline{b} =21\sqrt{2}\) ;

4. \(|\overline{a} |=11\) , \(|\overline{b} |=9\) , \(\overline{a} \,\overline{b} =0\) .

Решение.

1. \(\cos \alpha =\) [ ], значит, \(\alpha= \) [ ] \(\degree \) .

2. \(\cos \alpha =\) [ ], значит, \(\alpha= \) [ ] \(\degree \) .

3. \(\cos \alpha =\) [ ], значит, \(\alpha= \) [ ] \(\degree \) .

4. \(\cos \alpha =\) [ ], значит, \(\alpha =\) [ ] \(\degree \) .

Ответ:

1. [ ] \(\degree \) ; 2) [ ] \(\degree \) ; 3) [ ] \(\degree \) ; 4) [ ] \(\degree \) .