The equation of the plane passing through the points $(1,2,3)$, $(-1,4,2)$ and $(3,1,1)$ is

The equation of the plane passing through the points $(1,2,3)$, $(-1,4,2)$ and $(3,1,1)$ is
  1. $5 x+6 y+2 z-23=0$
  2. $5 x+y+2 z-13=0$
  3. $5 x+y+12 z-43=0$
  4. $5 x+y+12 z-43=0$

Solution

The required equation of plane $\begin{aligned} & \left|\begin{array}{ccc} x-1 & y-2 & z-3 \\ -1-1 & 4-2 & 2-3 \\ 3-1 & 1-2 & 1-3 \end{array}\right|=0 \\ & \Rightarrow\left|\begin{array}{ccc} x-1 & y-2 & z-3 \\ -2 & 2 & -1 \\ 2 & -1 & -2 \end{array}\right|=0 \\ & \Rightarrow-5(x-1)-6(y-2)-2(z-3)=0 \\ & \Rightarrow 5 x+6 y+2 z-23=0 \end{aligned}$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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