Question

Dados os pontos A(1,3,0) e B(-2,m,-2), calcular m para que |AB|=7

Answer 1

AB = B-A = (-2-1 ; m-3 ; -2-0)  = (-3; m-3 ; -2) 

$AB = (-3; (m-3) ; -2)\\\\|AB| = \sqrt{(-3)^2+(m-3)^2+(-2)^2} \\\\|AB|= \sqrt{9+4+(m^2-6m+9)} \\\\|AB|= \sqrt{m^2-6m+22} \\\\7=\sqrt{m^2-6m+22}\\\\7^2 =m^2-6m+22\\\\0=m^2-6m+22-49\\\\ \boxed{0=m^2-6m-27}$

aplicando bhaskara pra resover essa equaçao do segundo grau
m = -3 ou m=9