Question

Даны вершины треугольника ABC A(-1;4;6) B(-4;2;1) C(-1;2;5) найти косинус угла ABC

Answer 1

cosABC = (AB*BC)/(|AB|*|BC|)
AB = (-4-(-1), 2-4,1-6) = (-3,-2,-5)
BC = (-1-(-4), 2-2,5-1) = (3,0,4)

|AB| = sqrt(9+4+25) = sqrt(38)
|BC| = sqrt (9+0+16) = sqrt(25) = 5

cosABC = (-9+0-20)/(sqrt(38)*sqrt(5)) = -29/(sqrt(38)*sqrt(5))