The equation of the plane through the intersection of the planes $x+y+z=1$ and $2 x+3 y-z+4=0$ and parallel to $x-a x i s$ is

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Aicharya · Accepted Answer

Required equation is $(x+y+z-1)+\lambda(2 x+3 y-z+4)=0$ $\Rightarrow(1+2 \lambda) x+(1+3 \lambda) y+(1-\lambda) z+(4 \lambda-1)=0$ But plane is parallel to the $\mathrm{x}$-axis $\begin{aligned} & \Rightarrow \lambda=-\frac{1}{2} \ & \Rightarrow-\frac{1}{2} y+\frac{3}{2} z-3=0 \ & \Rightarrow y-3 z+6=0 \end{aligned}$

The equation of the plane through the intersection of the planes $x+y+z=1$ and $2 x+3 y-z+4=0$ and parallel…

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