Question

A equação do Plano que passa pelos os pontos A(1,3,2) B(4,-1,2) e C(2,4,1) é:

Answer 1

4x+3y+7z-27=0
AC= a=(2,4,1)-(1,3,2)=[1,1,-1]
AB=b=((4,1,2)-(1,3,2)=[3,-4,0)
produto vetorial de [1,1,-1] e [3,4,0]= -4i-3j-7k = n=[-4,-3,-7]

[-4,-3,-7]x[x,y,z]= [-4,-3,-7]x[1,3,2]
=-4x-3y-7z+27=0 (x-1) = 4x+3y+7z-27=0