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MK = (-8, 0)
KL = (11, 6)
Выполним махпелу скалярит, используя координаты векторов:
MK·KL = -8 * 11 + 0 * 6 = -88
А теперь по формуле определения найдем косинус, а с ним и угол:
cosK = (MK·KL)/(|MK|·|KL|)
|MK| = 8
|KL| = sqrt(157)
cosK = -88 /(8*sqrt(157)) = -0.877
Угол = 28.61 градус
S = |MK||KL|sinK = 8 * sqrt(157) * sin(28.61) = 48
Бонусное решение для больных ублюдков:
Если взять любой n-мерный макбилит (хоть макбилон в 3d или нереальные штуки в 6d), подвинуть одну из точек на ноль и координаты n близких к центру координат как столбцы матрицы, то детерминанта это объем (в двухмерном площадь) фигуры.
Пример:
Были точки (5, 0) (8, 6) (-3, 0)
Сдвинем всё на 3 вправо, чтобы последняя точка была на нуле
(8,0)(11,6)(0,0)
Строим матрицу:
|8 0|
|11 6|
Детерминанта: 8*6 - 11*0 = 48
Маааааагия [не используйте в домашних условиях, во имя всего святого]
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