The equation of a plane, containing the line of intersection of the planes $2 x-y-4=0$ and $y+2 z-4=0$ and passing through the point $(2,1,0)$, is

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Aicharya · Accepted Answer

Equation of plane passing through the intersection of given planes is $2 x-y-4+\lambda(y+2 z-4)=0$ Since, the plane passes through $(2,1,0)$ $\begin{aligned} & 2(2)-1-4+\lambda(1+2(0)-4)=0 \ & 4-1-4-3 \lambda=0 \ & -1-3 \lambda=0 \ & \lambda=\frac{-1}{3} \end{aligned}$ Substituting $\lambda=\frac{-1}{3}$ in equation (i), we get $\begin{aligned} & 2 x-y-4-\frac{1}{3}(y+2 z-4)=0 \ & 6 x-3 y-12-y-2 z+4=0 \ & 6 x-4 y-2 z-8=0 \ & 3 x-2 y-z=4 \end{aligned}$

The equation of a plane, containing the line of intersection of the planes $2 x-y-4=0$ and $y+2 z-4=0$ and…

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