Question

Determine o ponto P= (x,y,z) da interseção da reta r: {y=2x+3 z=3x-4 com plano π: 3x+5y-2z-9=0.

Answer 1

Boa noite Rafa!

Solução!

Vamos substituir as retas na equação do plano para determinarmos a terna.

$y=2x+3\\\\\\ z=3x-4\\\\\\ 3x+5y-2z-9=0\\\\\\\ Substituindo!\\\\\\\\\ 3x+5(2x+3)-2(3x-4)-9=0\\\\\\\ 3x+10x+15-6x+8-9=0\\\\\\\ 3x+10x-6x=-15-8+9\\\\\\\ 13x-6x=-23+9\\\\\\ 7x=-14\\\\\\ x= -\dfrac{14}{7}\\\\\\ \boxed{x=-2}$

Retomando as retas!

$y=2x+3\Rightarrow y=2(-2)+3\Rightarrow y=-4+3=-1\\\\\\ z=3x-4\Rightarrow z=3(-2)-4\Rightarrow z=-6-4=-10$


$\boxed{Resposta:Ponto(-2,-1,-10)}$


Boa noite!
Bons estudos!