НАЙТИ ПЛОЩАДЬ ТРЕУГОЛЬНИКА С ВЕРШИНАМИ А(1,-2,0)В(3,1,-1)С(-3,4,2)

НАЙТИ ПЛОЩАДЬ ТРЕУГОЛЬНИКА С ВЕРШИНАМИ А(1,-2,0)В(3,1,-1)С(-3,4,2)
- Предмет:
  Геометрия
- Автор:
  goose29
- 5 лет назад

Ответы 1

$AB=\{3-1;1-(-2);-1-0\}=\{2;3;-1\}\\ \\ AC=\{-3-1;4-(-2);2-0\}=\{-4;6;2\}$ $AB\cdot AC= \left|\begin{array}{ccc}i&j&k\\2&3&-1\\-4&6&2\end{array}ight|=i(3\cdot2+1\cdot6)-j(2\cdot2-1\cdot4)+\\ \\ +k(2\cdot6+3\cdot4)=12i-0j+24k\\ \\ |AB\cdot AC|=|\{12;0;24\}|= \sqrt{12^2+24^2} = \sqrt{12^2+12^2\cdot4} =12 \sqrt{5}$ Площадь $S= \frac{12 \sqrt{5} }{2} =6 \sqrt{5}$
- Автор:
  malachistone
- 5 лет назад
- 0
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НАЙТИ ПЛОЩАДЬ ТРЕУГОЛЬНИКА С ВЕРШИНАМИ А(1,-2,0)В(3,1,-1)С(-3,4,2)

Ответы 1

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