The equation of the plane, passing through the intersection of the planes $x+y+z=1$ and $2 x+3 y-z+4=0$ and…
The equation of the plane, passing through the intersection of the planes $x+y+z=1$ and $2 x+3 y-z+4=0$ and parallel to $Y$-axis is
$x+4 z-1=0$
$x+4 z-7=0$
$x-4 z+7=0$
$x-4 z+1=0$
Solution
Equation of plane passing through the intersection of given planes is
$\begin{aligned}
& (x+y+z-1)+\lambda(2 x+3 y-z+4)=0 \\
& \Rightarrow(1+2 \lambda) x+(1+3 \lambda) y+(1-\lambda) z+4 \lambda-1=0
\end{aligned}$ Since the plane is parallel to Y -axis.
$\begin{aligned}
\therefore \quad & 1+3 \lambda=0 \\
& \Rightarrow \lambda=\frac{-1}{3}
\end{aligned}$
$\therefore \quad$ Equation of the required plane is $x+4 \mathrm{z}-7=0$