Question

o comprimento do segmento de reta determinado por A (0,1,-2) e B (2,-3,1)

Answer 1

Olá

O calcular o comprimento, é a mesma coisa que calcular o módulo.


A = (0, 1, -2)
B = (2, -3, 1)

Criando o segmento AB

AB = B-A
AB = (2, -3, 1) - (0, 1, -2)
AB = (2-0, -3-1, 1-(-2))
AB = (2, -4, 3)

Calculando o módulo

$\mathsf{|AB|= \sqrt{(2)^2+(-4)^2+(3)^2} }\\\\\\\mathsf{|AB|= \sqrt{4+16+9} }\\\\\\\boxed{\mathsf{|AB|= \sqrt{29} }}\\\\\\\text{Em decimal}\\\\\\\boxed{\mathsf{|AB| = 5,38}}$