If the origin and the points $(1,2,3),(2,3,4)$ and $(x, y, z)$ are coplanar, then

If the origin and the points $(1,2,3),(2,3,4)$ and $(x, y, z)$ are coplanar, then
  1. $x-2 y+z=0$
  2. $x+y+z=6$
  3. $x-2 y+z+1=0$
  4. $z-2 x+y=0$

Solution

For give coplanar points, we write $\begin{aligned} &\left|\begin{array}{lll} 1 & 2 & 3 \\ 2 & 3 & 4 \\ x & y & z \end{array}\right|=0 \\ \therefore & x(8-9)-y(4-6)+z(3-4)=0 \\ \therefore &-x+2 y-z=0 \Rightarrow x-2 y+z=0 \end{aligned}$

Asked in: MHT CET 2020 (20 Oct Shift 2)

Practice more Line and Plane questions on Aicharya