The equation of the plane passing through the point $(2,2,1)$ and the intersection of the planes $x+2 y-3…

The equation of the plane passing through the point $(2,2,1)$ and the intersection of the planes $x+2 y-3 z+1=0$ and $3 x-2 y+4 z+3=0$ is
  1. $3 x+26 y+43 z+3=0$
  2. $3 x+26 y-43 z-3=0$
  3. $3 x-26 y-43 z-3=0$
  4. $3 x-26 y+43 z+3=0$

Solution

But it passes through $(2,2,1)$ $\begin{aligned} & \Rightarrow(2+2 \times 2-3 \times 1+1)+\lambda(3 \times 2-2 \times 2+4 \times 1+3)=0 \\ & \Rightarrow 4+9 \lambda=0 \\ & \Rightarrow \lambda=\frac{-4}{9} \text { in eq. (1) we get } \\ & 3 x-26 y+43 z+3=0 \end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 1)

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