Question

Find an equation of the plane. the plane through the point (2, 9, 4) and with normal vector 6i + j − k

Answer 1

1) n(6;1;-1)=n(A;B;C), point A(2;9;4)=A(x₀;y₀;z₀);
2) common view for a plane according the conditions is: A(x-x₀)+B(y-y₀)+C(z-z₀)=0;
3) after substituted coordinates: 6(x-2)+(y-9)-(z-4)=0; ⇒ 6x+y-z-17=0.