MHT CET · Maths · Three Dimensional Geometry
If the origin and the points \((1,2,3),(2,3,4)\) and \((x, y, z)\) are coplanar, then
- A \(x-2 y+z=0\)
- B \(x+y+z=6\)
- C \(x-2 y+z+1=0\)
- D \(z-2 x+y=0\)
Answer & Solution
Correct Answer
(A) \(x-2 y+z=0\)
Step-by-step Solution
Detailed explanation
For give coplanar points, we write
\(
\begin{aligned}
&\left|\begin{array}{lll}
1 & 2 & 3 \\
2 & 3 & 4 \\
x & y & z
\end{array}\right|=0 \\
\therefore & x(8-9)-y(4-6)+z(3-4)=0 \\
\therefore &-x+2 y-z=0 \Rightarrow x-2 y+z=0
\end{aligned}
\)
\(
\begin{aligned}
&\left|\begin{array}{lll}
1 & 2 & 3 \\
2 & 3 & 4 \\
x & y & z
\end{array}\right|=0 \\
\therefore & x(8-9)-y(4-6)+z(3-4)=0 \\
\therefore &-x+2 y-z=0 \Rightarrow x-2 y+z=0
\end{aligned}
\)
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