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Question: Answered & Verified by Expert
If the origin and the points $(1,2,3),(2,3,4)$ and $(x, y, z)$ are coplanar, then
MathematicsThree Dimensional GeometryMHT CETMHT CET 2020 (20 Oct Shift 2)
Options:
  • A $x-2 y+z=0$
  • B $x+y+z=6$
  • C $x-2 y+z+1=0$
  • D $z-2 x+y=0$
Solution:
2443 Upvotes Verified Answer
The correct answer is: $x-2 y+z=0$
For give coplanar points, we write
$$
\begin{aligned}
&\left|\begin{array}{lll}
1 & 2 & 3 \\
2 & 3 & 4 \\
x & y & z
\end{array}\right|=0 \\
\therefore & x(8-9)-y(4-6)+z(3-4)=0 \\
\therefore &-x+2 y-z=0 \Rightarrow x-2 y+z=0
\end{aligned}
$$

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