Equation of the plane passing through the point $(1,2,3)$ and parallel to the plane $2 x+3 y-4 z=0$
Equation of the plane passing through the point $(1,2,3)$ and parallel to the plane $2 x+3 y-4 z=0$
$2 x+3 y+4 z-8=0$
$2 x+3 y-4 z+4=0$
$2 x+3 y+4 z+4=0$
$2 x+3 y+4 z=20$
Solution
Required plane passes through $(1,2,3)$ and is parallel to plane $2 x+3 y-4 z=0$. Hence equation of required plane is
$2(x-1)+3(y-2)-4(z-3)=0 \Rightarrow 2 x+3 y-4 z+4=0$