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Находим основания медиан как середины сторон.
Основания медиан
x y z
A1 =BC/2 8 6 5
B1 =AC/2 7 5 5
C1 =AB/2 5 7 8.
Затем определяем векторы и модули (длины) медиан.
Векторы медиан
x y z Длина (модуль)
AA1 = 4 0 -3 √25 = 5
BB1 = 1 -3 -3 √19 = 4,358898944
CC1 = -5 3 6 √70 = 8,366600265.
ответ: медиана с наибольшей длиной СС1 = √70 = 8,3666.