Question

Dados os pontos A(2,-3,1) e B(4,5,-2), determinar o ponto P tal que AP=PB

Answer 1

AP = P - A = (x, y, z) - (2, -3, 1) = ( x - 2, y + 3, z -1)
PB = B - P = (4, 5, -2) - (x, y, z) = ( 4 - x, 5 - y, -2 - z)

AP = PB ↔ ( x - 2, y + 3, z -1) = ( 4 - x, 5 - y, -2 - z) ↔ (um sistema)

x - 2 = 4 - x
y + 3 =5 - y ↔
z - 1 = -2 - z

x = 3
↔ y = 1
z = -1/2