Question

Encontre e assinale a opção que representa a distância do ponto P (2,-1,2) em relação ao plano π: 2x-2y-z+3=0

Answer 1

Olá



P (2,-1,2)
π:  2x - 2y - z + 3 = 0



Fórmula:

$\displaystyle\mathsf{ d(P,\pi)~=~\frac{|ax~+~by~+~cz~+~d|}{ \sqrt{a^2+b^2+c^2} } }$



Substituindo os valores


$\displaystyle\mathsf{ d(P,\pi)~=~\frac{|2\cdot(2)~-~2\cdot(-1)~-~1\cdot(2)~+~3|}{ \sqrt{2^2+2^2+1^2} } }\\\\\\\\\mathsf{ d(P,\pi)~=~\frac{|4+2-2+3|}{ \sqrt{4+4+1} } }\\\\\\\\\mathsf{ d(P,\pi)~=~\frac{|7|}{ \sqrt{9} } }\\\\\\\\\boxed{\mathsf{ d(P,\pi)~=~\frac{7}{3 }~\approx~ 2,33 }}$