Question

Let the equation of the plane passing through the line $x-2 y-z-5=0=x+y+3 z-5$ and parallel to the line $x+y+2 z-7=0=2 x+3 y+z-2$ be $a x+b y+c z=65$ Then the distance of the point $(a, b, c)$ from the plane $2 x+2 y-z+16=0$ is _______

Answer 1

The correct answer is 9.
Equation of plane is
(x−2y−z−5)+b(x+y+3z−5)=0
∣∣​1+b12​−2+b13​−1+3b21​∣∣​=0
⇒b=12
∴ plane is 13x+10y+35z=65
Distance from given point to plane =9