MHT CET · Maths · Three Dimensional Geometry
The mirror image of the point \((1,2,3)\) in a plane is \(\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)\). Thus, the point lies on this plane.
- A \((1,-1,1)\)
- B \((-1,-1,1)\)
- C \((1,1,1)\)
- D \((-1,-1,-1)\)
Answer & Solution
Correct Answer
(A) \((1,-1,1)\)
Step-by-step Solution
Detailed explanation
\(\mathrm{M}\) is the midpoint.
\(
\therefore \quad \mathrm{M} \equiv\left(-\frac{2}{3}, \frac{1}{3}, \frac{4}{3}\right)
\)
D.r.s of \(\mathrm{AB}\) are \(\frac{-10}{3}, \frac{-10}{3}, \frac{-10}{3}\) i.e., \(1,1,1\)
Equation of plane is
\(
\begin{aligned}
& 1\left(x+\frac{2}{3}\right)+1\left(y-\frac{1}{3}\right)+1\left(z-\frac{4}{3}\right)=0 \\
& \Rightarrow x+y+z=1
\end{aligned}
\)
Option (A) satisfies this equation of the plane.
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